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Engineering Mechanics Dynamics 14th Global Edition Hibbeler - Solutions

12–226. The man can row the boat in still water with a speed of 5 m>s. If the river is flowing at 2 m>s, determine the speed of the boat and the angle u he must direct the boat so that it travels from A to B. 5 m/s 50 m -2 m/s -25 m- Prob. 12-226
12–225. At the instant shown, car A has a speed of 20 km>h, which is being increased at the rate of 300 km>h2 as the car enters the expressway. At the same instant, car B is decelerating at 250 km>h2 while traveling forward at 100 km>h. Determine the velocity and acceleration of A
*12–224. At the instant shown car A is traveling with a velocity of 30 m>s and has an acceleration of 2 m>s2 along the highway. At the same instant B is traveling on the trumpet interchange curve with a speed of 15 m>s, which is decreasing at 0.8 m>s2. Determine the relative velocity
12–223. A man can row a boat at 5 m>s in still water. He wishes to cross a 50-m-wide river to point B, 50 m downstream. If the river flows with a velocity of 2 m>s, determine the speed of the boat and the time needed to make the crossing. A -50 m- +2 m/s 50 m Prob. 12-223 B
12–222. Two boats leave the shore at the same time and travel in the directions shown. If vA = 10 m>s and vB = 15 m>s, determine the velocity of boat A with respect to boat B. How long after leaving the shore will the boats be 600 m apart? VA = 10 m/s v = 15 m/s B 130 45 Prob. 12-222
12–221. A car is traveling north along a straight road at 50 km>h. An instrument in the car indicates that the wind is coming from the east. If the car’s speed is 80 km>h, the instrument indicates that the wind is coming from the northeast.Determine the speed and direction of the wind.
*12–220. Two planes, A and B, are flying at the same altitude. If their velocities are vA = 500 km>h and vB = 700 km>h such that the angle between their straightline courses is u = 60, determine the velocity of plane B with respect to plane A. VB = 700 km/h B 60 Prob. 12-220 V = 500 km/h
12–219. The car is traveling at a constant speed of 100 km>h. If the rain is falling at 6 m>s in the direction shown, determine the velocity of the rain as seen by the driver. A vc 100 km/h 30 Prob. 12-219
12–218. The boat can travel with a speed of 16 km>h in still water. The point of destination is located along the dashed line. If the water is moving at 4 km>h, determine the bearing angle u at which the boat must travel to stay on course. vw=4 km/h 70 Prob. 12-218
12–217. At the instant shown, the car at A is traveling at 10 m>s around the curve while increasing its speed at 5 m>s2.The car at B is traveling at 18.5 m>s along the straightaway and increasing its speed at 2 m>s2. Determine the relative velocity and relative acceleration of A with
*12–216. If block B is moving down with a velocity vB and has an acceleration aB, determine the velocity and acceleration of block A in terms of the parameters shown. SA Th Prob. 12-216 B VB, 3B
12–215. The motor draws in the cord at B with an acceleration of aB = 2 m>s2. When sA = 1.5 m, vB = 6 m>s.Determine the velocity and acceleration of the collar at this instant. 2 m SA Prob. 12-215 A B
12–214. The man pulls the boy up to the tree limb C by walking backward. If he starts from rest when xA = 0 and moves backward with a constant acceleration aA = 0.2 m/s2, determine the speed of the boy at the instant yB = 4 m.Neglect the size of the limb. When xA = 0, yB = 8 m, so that A and B
12–213. The man pulls the boy up to the tree limb C by walking backward at a constant speed of 1.5 m>s. Determine the speed at which the boy is being lifted at the instant xA = 4 m.Neglect the size of the limb. When xA = 0, yB = 8 m, so that A and B are coincident, i.e., the rope is 16 m long.
*12–212. The roller at A is moving with a velocity of vA = 4 m>s and has an acceleration of aA = 2 m>s2 when xA = 3 m. Determine the velocity and acceleration of block B at this instant. V = 4 m/s 4 m Prob. 12-212 B
12–211. The crate C is being lifted by moving the roller at A downward with a constant speed of vA = 2 m>s along the guide. Determine the velocity and acceleration of the crate at the instant s = 1 m. When the roller is at B, the crate rests on the ground. Neglect the size of the pulley in the
12–210. If the truck travels at a constant speed of vT = 1.8 m>s, determine the speed of the crate for any angle u of the rope. The rope has a length of 30 m and passes over a pulley of negligible size at A. Hint: Relate the coordinates xT and xC to the length of the rope and take the time
12–209. If the hydraulic cylinder H draws in rod BC at 1 m>s, determine the speed of slider A. H B C A Prob. 12-209
*12–208. The cable at A is being drawn toward the motor at vA = 8 m>s. Determine the velocity of the block. B A Probs. 12-207/208
12–207. Determine the time needed for the load at B to attain a speed of 10 m>s, starting from rest, if the cable is drawn into the motor with an acceleration of 3 m>s2. B A Probs. 12-207/208
12–206. The motor draws in the cable at C with a constant velocity of vC = 4 m>s. The motor draws in the cable at D with a constant acceleration of aD = 8 m>s2. If vD = 0 when t = 0, determine (a) the time needed for block A to rise 3 m, and (b) the relative velocity of block A with respect
12–205. If the end A of the cable is moving at vA = 3 m>s, determine the speed of block B. C G D A V = 3 m/s B Prob. 12-205
*12–204. Determine the speed of block A if the end of the rope is pulled down with a speed of 4 m>s. A 4 m/s B Prob. 12-204
12–203. If block A is moving downward with a speed of 2 m>s while C is moving up at 1 m>s, determine the speed of block B. A B C Prob. 12-203
12–202. Determine the speed of the block at B. 6 m/s A Prob. 12-202 B
12–201. The motor at C pulls in the cable with an acceleration aC = (3t2) m>s2, where t is in seconds. The motor at D draws in its cable at aD = 5 m>s2. If both motors start at the same instant from rest when d = 3 m, determine(a) the time needed for d = 0, and (b) the velocities of blocks
12–200. If the end of the cable at A is pulled down with a speed of 2 m>s, determine the speed at which block B rises. D 2 m/s A B Prob. 12-200
12–199. Starting from rest, the cable can be wound onto the drum of the motor at a rate of vA = (3t2) m>s, where t is in seconds. Determine the time needed to lift the load 7 m. D A C B Probs. 12-198/199
12–198. Determine the constant speed at which the cable at A must be drawn in by the motor in order to hoist the load 6 m in 1.5 s.
12–197. If the end A of the cable is moving upwards at vA =14 m>s, determine the speed of block B. F VA 14 m/s D E B Prob. 12-197
*12–196. Determine the displacement of the log if the truck at C pulls the cable 1.2 m to the right. B Prob. 12-196
12–195. If the end of the cable at A is pulled down with a speed of 5 m>s, determine the speed at which block B rises. A 5 m/s B Prob. 12-195
12–194. When u = 2/3p rad, the angular velocity and angular acceleration of the circular plate are u#= 1.5 rad/s and u$= 3 rad/s2, respectively. Determine the magnitudes of the velocity and acceleration of the rod AB at this instant. B T= = (10 + 5002) mm- Probs. 12-193/194
12–193. If the circular plate rotates clockwise with a constant angular velocity of u#= 1.5 rad/s, determine the magnitudes of the velocity and acceleration of the follower rod AB when u = 2/3p rad. B T= = (10 + 5002) mm- Probs. 12-193/194
*12–192. When u = 15°, the car has a speed of 50 m>s which is increasing at 6 m>s2. Determine the angular velocity of the camera tracking the car at this instant. (100 cos 20) m Probs. 12-191/192
12–191. The driver of the car maintains a constant speed of 40 m>s. Determine the angular velocity of the camera tracking the car when u = 15°. (100 cos 20) m Probs. 12-191/192
12–189. For a short distance the train travels along a track having the shape of a spiral, r = (1000/u) m, where u is in radians. If it maintains a constant speed v = 20 m>s, determine the radial and transverse components of its velocity when u = (9p/4) rad.12–190. For a short distance the
*12–188. The double collar C is pin connected together such that one collar slides over the fixed rod and the other slides over the rotating rod AB. If the mechanism is to be designed so that the largest speed given to the collar is 6 m>s, determine the required constant angular velocity u#of
12–187. The double collar C is pin connected together such that one collar slides over the fixed rod and the other slides over the rotating rod AB. If the angular velocity of AB is given as u#= (e0.5 t2) rad>s, where t is in seconds, and the path defined by the fixed rod is r = |(0.4 sin u +
12–186. A truck is traveling along the horizontal circular curve of radius r = 60 m with a speed of 20 m>s which is increasing at 3 m>s2. Determine the truck’s radial and transverse components of acceleration. r = 60 m Probs. 12-185/186
12–185. A truck is traveling along the horizontal circular curve of radius r = 60 m with a constant speed v = 20 m>s.Determine the angular rate of rotation u#of the radial line r and the magnitude of the truck’s acceleration.
*12–184. At the instant u = 30°, the cam rotates with a clockwise angular velocity of u#= 5 rad>s and, angular acceleration of u$= 6 rad/s2. Determine the magnitudes of the velocity and acceleration of the follower rod AB at this instant. The surface of the cam has a shape of a limaçon
12–183. If the cam rotates clockwise with a constant angular velocity of u#= 5 rad>s, determine the magnitudes of the velocity and acceleration of the follower rod AB at the instant u = 30°. The surface of the cam has a shape of limaçon defined by r = (200 + 100 cos u) mm. =(200+100 cos 0)
12–182. The slotted arm AB drives pin C through the spiral groove described by the equation r = (1.5 u) m, where u is in radians. If the arm starts from rest when u = 60° and is driven at an angular velocity of u#= (4t) rad>s, where t is in seconds, determine the radial and transverse
12–181. The slotted arm AB drives pin C through the spiral groove described by the equation r = au. If the angular velocity is constant at u#, determine the radial and transverse components of velocity and acceleration of the pin. C Probs. 12-181/182
*12–180. Determine the magnitude of the acceleration of the slider blocks in Prob. 12–179 when u = 120°. = 5 rad/s B r 100 (2 cos 0) m Probs. 12-179/180
12–179. The rod OA rotates counterclockwise with a constant angular velocity of u#= 5 rad>s. Two pin-connected slider blocks, located at B, move freely on OA and the curved rod whose shape is a limaçon described by the equation r = 100(2 − cos u) mm. Determine the speed of the slider blocks
12–178. Determine the magnitude of the acceleration of the slider blocks in Prob. 12–177 when u = 150°. A B 6 rad/s 400 mm -0. - 600 mm 200 mm Probs. 12-177/178
12–177. The rod OA rotates clockwise with a constant angular velocity of 6 rad>s. Two pin-connected slider blocks, located at B, move freely on OA and the curved rod whose shape is a limaçon described by the equation r = 200(2 − cos u) mm. Determine the speed of the slider blocks at the
12–176. The pin follows the path described by the equation r = (0.2 + 0.15 cos u) m. At the instant u = 30, u #= 0.7 rad/s and u$= 0.5 rad/s2. Determine the magnitudes of the pin’s velocity and acceleration at this instant. Neglect the size of the pin. 7=0.2+0.15 cos 0 = 0.7 rad/s Prob. 12-176
12–175. A block moves outward along the slot in the platform with a speed of r # = (4t) m>s, where t is in seconds.The platform rotates at a constant rate of 6 rad>s. If the block starts from rest at the center, determine the magnitudes of its velocity and acceleration when t = 1 s. Prob.
12–174. The car travels around the circular track such that its transverse component is u = (0.006t2) rad, where t is in seconds. Determine the car’s radial and transverse components of velocity and acceleration at the instant t = 4 s. T=(400 cos 0) n Probs. 12-173/174
12–173. The car travels around the circular track with a constant speed of 20 m>s. Determine the car’s radial and transverse components of velocity and acceleration at the instant u = p>4 rad. T=(400 cos 0) n Probs. 12-173/174
12–172. A cameraman standing at A is following the movement of a race car, B, which is traveling around a curved track at a constant speed of 30 m>s. Determine the angular rate u#at which the man must turn in order to keep the camera directed on the car at the instant u = 30°. 20 m VB = 30
12–171. Solve Prob. 12–170, if the cam has an angular acceleration of u$= 2 rad>s2 when its angular velocity is u #= 4 rad>s at u = 30°. 0 = 4 rad/s Probs. 12-170/171 r = 400.059
12–170. The partial surface of the cam is that of a logarithmic spiral r = (40e0.05u) mm, where u is in radians. If the cam is rotating at a constant angular rate of u#= 4 rad/s, determine the magnitudes of the velocity and acceleration of the follower rod at the instant u = 30°. 0 = 4 rad/s
12–169. At the instant shown, the man is twirling a hose over his head with an angular velocity u#= 2 rad>s and an angular acceleration u$= 3 rad>s2. If it is assumed that the hose lies in a horizontal plane, and water is flowing through it at a constant rate of 3 m>s, determine the
*12–168. At the instant shown, the watersprinkler is rotating with an angular speed u#= 2 rad>s and an angular acceleration u$= 3 rad>s2. If the nozzle lies in the vertical plane and water is flowing through it at a constant rate of 3 m>s, determine the magnitudes of the velocity and
12–167. The slotted link is pinned at O, and as a result of the constant angular velocity u#= 3 rad>s it drives the peg P for a short distance along the spiral guide r = (0.4 u) m, where u is in radians. Determine the radial and transverse components of the velocity and acceleration of P at
12–166. A particle is moving along a circular path having a 400-mm radius. Its position as a function of time is given by u = (2t2) rad, where t is in seconds. Determine the magnitude of the particle’s acceleration when u = 30°. The particle starts from rest when u = 0°.
12–165. The time rate of change of acceleration is referred to as the jerk, which is often used as a means of measuring passenger discomfort. Calculate this vector, a # , in terms of its cylindrical components, using Eq. 12–32.
*12–164. The small washer is sliding down the cord OA.When it is at the midpoint, its speed is 28 m>s and its acceleration is 7 m>s2. Express the velocity and acceleration of the washer at this point in terms of its cylindrical components. Z A 3 m x Prob. 12-164 6 m y 2 m
12–163. A radar gun at O rotates with the angular velocity of u#= 0.1 rad>s and angular acceleration of u$=0.025 rad>s2, at the instant u = 45°, as it follows the motion of the car traveling along the circular road having a radius of r = 200 m. Determine the magnitudes of velocity and
12–162. If a particle moves along a path such that r = (eat) m and u = t, where t is in seconds, plot the path r = f(u), and determine the particle’s radial and transverse components of velocity and acceleration.
12–161. If a particle’s position is described by the polar coordinates r = (2 sin 2u) m and u = (4t) rad, and where t is in seconds, determine the radial and transverse components of its velocity and acceleration when t = 1 s.
*12–160. The box slides down the helical ramp such that r = 0.5 m, u = (0.5t3) rad, and z = (2 - 0.2t2) m, where t is in seconds. Determine the magnitudes of the velocity and acceleration of the box at the instant u = 2p rad. (0.5 m Probs. 12-159/160
12–159. The box slides down the helical ramp with a constant speed of v = 2 m>s. Determine the magnitude of its acceleration. The ramp descends a vertical distance of 1 m for every full revolution.The mean radius of the ramp is r = 0.5 m. (0.5 m Probs. 12-159/160
12–158. For a short time a rocket travels up and to the right at a constant speed of 800 m>s along the parabolic path y = 600 - 35x2. Determine the radial and transverse components of velocity of the rocket at the instant u = 60°, where u is measured counterclockwise from the x axis.
12–157. A particle moves along a circular path of radius 300 mm. If its angular velocity is u#= (2t2) rad>s, where t is in seconds, determine the magnitude of the particle’s acceleration when t = 2 s.
*12–156. A particle travels around a limaçon, defined by the equation r = b - a cos u, where a and b are constants.Determine the particle’s radial and transverse components of velocity and acceleration as a function of u and its time derivatives.
12–155. If a particle’s position is described by the polar coordinates r = 4(1 + sin t) m and u = (2e-t) rad, where t is in seconds and the argument for the sine is in radians, determine the radial and transverse components of the particle’s velocity and acceleration when t = 2 s.
12–154. A particle P travels along an elliptical spiral path such that its position vector r is defined by r = 52 cos(0.1t)i + 1.5 sin(0.1t)j + (2t)k6 m, where t is in seconds and the arguments for the sine and cosine are given in radians. When t = 8 s, determine the coordinate direction anglesa,
12–153. When the bicycle passes point A, it has a speed of 6 m>s, which is increasing at the rate of v # = (0.5) m>s2.Determine the magnitude of its acceleration when it is at point A. +50 m A y = 12 In () 20 Probs. 12-152/153 x
*12–152. A particle P moves along the curve y = (x2 - 4) m with a constant speed of 5 m>s. Determine the point on the curve where the maximum magnitude of acceleration occurs and compute its value.
12–151. Particles A and B are traveling around a circular track at a speed of 8 m>s at the instant shown. If the speed of B is increasing by (at)B = 4 m>s2, and at the same instant A has an increase in speed of (at)A = 0.8t m>s2, determine how long it takes for a collision to occur. What
12–150. Particles A and B are traveling counterclockwise around a circular track at a constant speed of 8 m>s. If at the instant shown the speed of A begins to increase by(at)A = (0.4sA) m>s2, where sA is in meters, determine the distance measured counterclockwise along the track from B to
12–149. The jet plane is traveling with a constant speed of 110 m>s along the curved path. Determine the magnitude of the acceleration of the plane at the instant it reaches point A(y = 0). y -80 m- y = 15 In(0) Probs. 12-148/149 x
*12–148. The jet plane is traveling with a speed of 120 m>s which is decreasing at 40 m>s2 when it reaches point A.Determine the magnitude of its acceleration when it is at this point. Also, specify the direction of flight, measured from the x axis.
12–147. The train passes point A with a speed of 30 m>s and begins to decrease its speed at a constant rate of at = - 0.25 m>s2. Determine the magnitude of the acceleration of the train when it reaches point B, where sAB = 412 m. A y = 200 e1000 400 m- Probs. 12-146/147 x
12–146. The train passes point B with a speed of 20 m>s which is decreasing at at = - 0.5 m>s2. Determine the magnitude of acceleration of the train at this point. A y y = 200 e1000 -400 m- Probs. 12-146/147 x
12–145. The particle travels with a constant speed of 300 mm>s along the curve. Determine the particle’s acceleration when it is located at point (200 mm, 100 mm)and sketch this vector on the curve. y (mm) 20(103) x P Prob. 12-145 x (mm)
*12–144. Cars move around the “traffic circle” which is in the shape of an ellipse. If the speed limit is posted at 60 km>h, determine the maximum acceleration experienced by the passengers. (60) (40) 40 m 60 m Probs. 12-143/144
12–143. Cars move around the “traffic circle” which is in the shape of an ellipse. If the speed limit is posted at 60 km>h, determine the minimum acceleration experienced by the passengers. (60) (40) 40 m 60 m Probs. 12-143/144
12–142. The ball is kicked with an initial speed vA = 8 m>s at an angle uA = 40 with the horizontal. Find the equation of the path, y = f(x), and then determine the ball’s velocity and the normal and tangential components of its acceleration when t = 0.25 s. A VA = 8 m/s 0 = 40 -x Prob.
12–141. The race car has an initial speed vA = 15 m>s at A.If it increases its speed along the circular track at the rate at = (0.4s) m>s2, where s is in meters, determine the time needed for the car to travel 20 m. Take r = 150 m. Prob. 12-141
*12–140. The motorcycle travels along the elliptical track at a constant speed v. Determine its smallest acceleration if a 7 b. Probs. 12-139/140 a 1 b
12–139. The motorcycle travels along the elliptical track at a constant speed v. Determine its greatest acceleration if a 7 b. b. Probs. 12-139/140 a 1 b
12–138. The ball is ejected horizontally from the tube with a speed of 8 m>s. Find the equation of the path, y = f(x), and then find the ball’s velocity and the normal and tangential components of acceleration when t = 0.25 s. V = 8 m/s -x Prob. 12-138
12–137. When t = 0, the train has a speed of 8 m>s, which is increasing at 0.5 m>s2. Determine the magnitude of the acceleration of the engine when it reaches point A, at t = 20 s. Here the radius of curvature of the tracks is rA = 400 m. v = 8 m/s Prob. 12-137 A
*12–136. The motorcycle is traveling at a constant speed of 60 km>h. Determine the magnitude of its acceleration when it is at point A. 25 m- Prob. 12-136 2x -x
12–135. Starting from rest, a bicyclist travels around a horizontal circular path, r = 10 m, at a speed of v = (0.09t2 + 0.1t) m>s, where t is in seconds. Determine the magnitudes of his velocity and acceleration when he has traveled s = 3 m.
12–134. A boat is traveling along a circular path having a radius of 20 m. Determine the magnitude of the boat’s acceleration when the speed is v = 5 m>s and the rate of increase in the speed is v # = 2 m>s2.
12–133. At a given instant the jet plane has a speed of 550 m>s and an acceleration of 50 m>s2 acting in the direction shown. Determine the rate of increase in the plane’s speed, and also the radius of curvature r of the path. 550 m/s 70 a = 50 m/s Prob. 12-133
*12–132. The motorcycle is traveling at 40 m>s when it is at A. If the speed is then decreased at v # = - (0.05 s) m>s2, where s is in meters measured from A, determine its speed and acceleration when it reaches B. -60 150 m B 150 m Prob. 12-132
12–131. A particle travels around a circular path having a radius of 50 m. If it is initially traveling with a speed of 10 m>s and its speed then increases at a rate of v #= (0.05 v) m>s2, determine the magnitude of the particle’s acceleration four seconds later.
12–130. The position of a particle traveling along a curved path is s = (3t3 - 4t2 + 4) m, where t is in seconds. When t = 2 s, the particle is at a position on the path where the radius of curvature is 25 m. Determine the magnitude of the particle’s acceleration at this instant.
12–129. The box of negligible size is sliding down along a curved path defined by the parabola y = 0.4x2. When it is at A(xA = 2 m, yA = 1.6 m), the speed is v = 8 m>s and the increase in speed is dv>dt = 4 m>s2. Determine the magnitude of the acceleration of the box at this instant. y =
*12–128. If the roller coaster starts from rest at A and its speed increases at at = (6 - 0.06s) m>s2, determine the magnitude of its acceleration when it reaches B where sB = 40 m. 30 m- Probs. 12-127/128 100
12–127. When the roller coaster is at B, it has a speed of 25 m>s, which is increasing at at = 3 m>s2. Determine the magnitude of the acceleration of the roller coaster at this instant and the direction angle it makes with the x axis. 30 m- Probs. 12-127/128 100
12–126. At a given instant the train engine at E has a speed of 20 m>s and an acceleration of 14 m>s2 acting in the direction shown. Determine the rate of increase in the train’s speed and the radius of curvature r of the path. a 14 m/s- 75 v = 20 m/s Prob. 12-126

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