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engineering
engineering mechanics statics
Engineering Mechanics Statics & Dynamics 15th Edition Russell C. Hibbeler - Solutions
A freight train starts from rest and travels with a constant acceleration of 0.5 ft/s². After a time t' it maintains a constant speed so that when t = 160 s it has traveled 2000 ft. Determine the time t' and draw the v-t graph for the motion.
Water is sprayed at an angle of 90° from the slope at 20 m/s. Determine the range R. R VB = 20 m/s
If the effects of atmospheric resistance are accounted for, a freely falling body has an acceleration defined by the equation, a = 9.81[1- v²(10-4)] m/s², where v is in m/s and the positive direction is downward. If the body is released from rest at a very high altitude, determine (a)
A ball is thrown with an upward velocity of 5 m/s from the top of a 10-m-high building. One second later another ball is thrown upward from the ground with a velocity of 10 m/s. Determine the height from the ground where the two balls pass each other.
The platform is rotating about the vertical axis such that at any instant its angular position is = (4/³/2) rad,where t is in seconds. A ball rolls outward along the radialgroove so that its position is r = (0.1t³) m, where t is inseconds. Determine the magnitudes of the velocity andacceleration
The car travels up the hill with a speed of v = (0.2s) m/s, where s is in meters, measured from A. Determine the magnitude of its acceleration when it is at s = 50 m, where ρ = 500 m. A s = 50 m- n -X
The car has a speed of 55 ft/s. Determine the angular velocity θ of the radial line OA at this instant. Ox r = 400 ft COMO A
Ball A is thrown vertically upward from the top of a 30-m- high building with an initial velocity of 5 m/s. At the same instant another ball B is thrown upward from the ground with an initial velocity of 20 m/s. Determine the height from the ground and the time at which they pass.
As a body is projected to a high altitude above the earth's surface, the variation of the acceleration of gravity with respect to altitude y must be taken into account. Neglecting air resistance, this acceleration is determined from the formula a = −g0[R²/(R + y)²], where g0 is the constant
The elevator starts from rest at the first floor of the building. It can accelerate at 5 ft/s² and then decelerate at 2 ft/s². Determine the shortest time it takes to reach a floor 40 ft above the ground. The elevator starts from rest and then stops. Draw the a-t, v-t, and s-t graphs for the
Accounting for the variation of gravitational acceleration a with respect to altitude y (see Prob. 12–33), derive an equation that relates the velocity of a freely falling particle to its altitude. Assume that the particle is released from rest at an altitude y0 from the earth’s surface. With
A car starting from rest moves along a straight track with an acceleration as shown. Determine the time t for the car to reach a speed of 50 m/s and construct the v–t graph that describes the motion until the time t. a (m/s²) 8 10 t t (s)
Two rockets start from rest at the same elevation. Rocket A accelerates vertically at 20 m/s2 for 12 s and then maintains a constant speed. Rocket B accelerates at 15 m/s2 until reaching a constant speed of 150 m/s. Construct the a–t, v–t, and s–t graphs for each rocket until t = 20 s. What
The motion of a jet plane just after landing on a runway is described by the a–t graph. Determine the time t when the jet plane stops. Construct the v–t and s–t graphs for the motion. Here s = 0, and v = 300 ft/s when t = 0. a (ft/s²) -10 -20 10 20 000000 -t (s)
A particle starts from s = 0 and travels along a straight line with a velocity v = (t²- 4t+ 3) m/s, where t is in seconds. Construct the v-t and a-t graphs for the time interval 0 ≤ t ≤ 4 s.
The v-t graph for a particle moving through an electric field from one plate to another has the shape shown in the figure. The acceleration and deceleration that occur are constant and both have a magnitude of 4 m/s². If the plates are spaced 200 mm apart, determine the maximum velocity vmax and
If the position of a particle is defined by s = [2 sin (π/5)t + 4] m, where t is in seconds, constructthe s-t, v-t, and a-t graphs for 0 ≤ t ≤ 10 s.
An airplane starts from rest, travels 5000 ft down a runway, and after uniform acceleration, takes off with a speed of 162 mi/h. It then climbs in a straight line with a uniform acceleration of 3 ft/s² until it reaches a constant speed of 220 mi/h. Draw the s-t, v-t, and a-t graphs that describe
Car A is traveling with a constant speed of 80 km/h due north, while car B is traveling with a constant speed of 100 km/h due east. Determine the velocity of car B relative to car A. FORD B 100 km/h 2 km 45° COMO 80 km/h
The v–t graph for a particle moving through an electric field from one plate to another has the shape shown in the figure, where t' = 0.2 s and vmax = 10 m/s. Draw the s–t and a–t graphs for the particle. When t = t' /2 the particle is at s = 0.5 m. Vmax V ť/2 S Smax t
Two planes A and B are traveling with the constant velocities shown. Determine the magnitude and direction of the velocity of B relative to A. Ug = 800 km/h VA = 650 km/h B 60°
The a–s graph for a rocket moving along a straight track has been experimentally determined. If the rocket starts at s = 0 when v = 0, determine its speed when it is at s = 75 ft, and 125 ft, respectively. Use Simpson’s rule with n = 100 to evaluate v at s = 125 ft. a (ft/s²) 5 a = 5 + 6(√5
The boats A and B travel with constant speeds of VA = 15 m/s and VB = 10 m/s when they leave the pier at O at the same time. Determine the distance between them when t = 4 s. У UB = 10 m/s 30° 30° B A va = 15 m/s X
The rocket has an acceleration described by the graph. If it starts from rest, construct the v-t and s-t graphs for the motion for the time interval 0 ≤ t ≤ 14s. a(m/s²) 38 18. a² = 36t a = 4t - 18 14 - t(s)
The s–t graph for a train has been determined experimentally. From the data, construct the v–t and a–t graphs for the motion. s (m) 600 360 s 24t360- s = 0.41² 30 40 Hote -t (s)
The jet car is originally traveling at a velocity of 10 m/s when it is subjected to the acceleration shown. Determine the car’s maximum velocity and the time t when it stops. When t = 0, s = 0. a (m/s²) 6 -4 15 t (s)
From experimental data, the motion of a jet plane while traveling along a runway is defined by the v–t graph shown. Construct the s–t and a–t graphs for the motion. v (m/s) 80 10 40 -t (s)
The v-t graph for a train has been experimentally determined. From the data, construct the s-t and a-t graphs for the motion for 0 ≤ t ≤ 180 s. When t=0,s=0. v (m/s) 10 6 60 120 180 ... ... t (s)
An airplane lands on the straight runway, originally traveling at 110 ft/s when s = 0. If it is subjected to the decelerations shown, determine the time t' needed to stop the plane and construct the s-t graph for the motion. a (ft/s²) -3 -8 5 15 000000000 20 t' t(s)
Starting from rest at s = 0, a boat travels in a straight line with the acceleration shown by the a-s graph. Determine the boat's speed when s = 50 ft, 100 ft, and 150 ft. a (ft/s²) 8 6 100 150 -s (ft)
A motorcycle starts from rest at s = 0 and travels along a straight road with the speed shown by the v–t graph. Determine the total distance the motorcycle travels until it stops when t = 15 s. Also plot the a–t and s–t graphs. v (m/s) 5 v = 1.25t 4 y = 5 10 v = -1 + 15 15 t(s)
A motorcycle starts from rest at s = 0 and travels along a straight road with the speed shown by the v–t graph. Determine the motorcycle’s acceleration and position when t = 8 s and t = 12 s. v (m/s) 5 v = 1.25t v = 5 4 10 v=-1 + 15 15 t(s)
Starting from rest at s = 0, a boat travels in a straight line with the acceleration shown by the a–s graph. Construct the v–s graph. a (ft/s²) 100 150 s (ft)
The v–t graph for the motion of a car as it moves along a straight road is shown. Draw the s–t and a–t graphs. Also determine the average speed and the distance traveled for the 15-s time interval. When t = 0, s = 0. v (m/s) 15 V= = 0.6t2 5 60 15 t (s)
The speed of a train during the first minute has been recorded as follows:Plot the v-t graph, approximating the curve as straight-line segments between the given points. Determine the total distance traveled. t (s) v (m/s) 0 20 0 16 40 21 60 24
A motorcyclist starting from rest travels along a straight road and for 10 s has an acceleration as shown. Draw the v-t graph that describes the motion and find the distance traveled in 10 s. a (m/s2) 6 =ㅎㅎ a = 9 10 -t (s)
The boat is originally traveling at a speed of 8 m/s when it is subjected to the acceleration shown in the graph. Determine the boat’s maximum speed and the time t when it stops. - t(s) 1 24 9 + 1/²/3 - = 9 a (m/s²)
The v - s graph of a cyclist traveling along a straight road is shown. Construct the a-s graph. v (ft/s) 15-- v= 0.1s + 5. 5- 100 v=-0.04s + 19 350 S (ft)
The jet bike is moving along a straight road with the speed described by the v-s graph. Construct the a-s graph. v(m/s) 75. 15- v = 55¹/2 225 -v = -0.2s + 120 525 s(m)
The a–s graph for a freight train is given for the first 200 m of its motion. Plot the v–s graph. The train starts from rest. a (m/s?) 2 100 200 -s(m)
A man riding upward in a freight elevator accidentally drops a package off the elevator when it is 100 ft from the ground. If the elevator maintains a constant upward speed of 4 ft/s, determine how high the elevator is from the ground the instant the package hits the ground. Draw the v–t curve
Two cars start from rest side by side and travel along a straight road. Car A accelerates at 4 m/s² for 10 s and then maintains a constant speed. Car B accelerates at 5 m/s² until reaching a constant speed of 25 m/s and then maintains this speed. Construct the a-t, v-t, and s-t graphs for each
The jet plane starts from rest at s = 0 and is subjected to the acceleration shown. Construct the v–s graph and determine the time needed to travel 500 ft down the runway. a (ft/s²) 75 a = 75 -0.15s 500 s (ft)
The water sprinkler, positioned at the base of a hill, releases a stream of water with a velocity of 15 ft/s as shown. Determine the point B(x, y) where the water strikes the ground on the hill. Assume that the hill is defined by the equation y = (0.05x2) ft and neglect the size of the sprinkler.
If the position of a particle is defined as S = (5t - 31²) ft, where t is in seconds, construct the s-t, v-t, and a-t graphs for 0 ≤ t ≤ 2.5s.
A particle travels along the curve from A to B in 5 s. It takes 8 s for it to go from B to C and then 10 s to go from C to A. Determine its average speed when it goes around the closed path. y A 20 m B -30 m C X
A rocket is fired from rest at x = 0 and travels along a parabolic trajectory described by y2 = [120(103)x] m. If the x component of acceleration iswhere t is in seconds,determine the magnitudes of the rocket’s velocity and acceleration when t = 10 s. = ax 1 (71) 1/s2, 4
A particle travels along the curve from A to B in 2 s. It takes 4 s for it to go from B to C and then 3 s to go from C to D. Determine its average speed when it goes from A to D. y A 10 m B 15 m. C 5 m D X
If the velocity of a particle is defined as v(t) = {0.8t2i + 12t1/2j + 5k} m/s, determine the magnitude and coordinate direction angles α, β, γ of the particle’s acceleration when t = 2 s.
A particle moves along the curve y = e2x such that its velocity has a constant magnitude of v = 4 ft/s. Determine the x and y components of velocity when the particle is at y = 5 ft.
A particle travels along the parabolic path y = bx². If its component of velocity along the y axis is vy, = ct², determinethe x and y components of the particle's acceleration. Here band c are constants.
A car traveling along the road has the velocities indicated in the figure when it arrives at points A, B, and C. If it takes 10 s to go from A to B, and then 15 s to go from B to C, determine the average acceleration between points A and B and between points A and C. y 40 m/s X 416 m/s B 12 m/s A
A particle travels along the circular path x2 + y2 = r2. If the y component of the particle’s velocity is vy = 2r cos 2t, determine the x and y components of its acceleration at any instant.
The particle travels along the path defined by the parabola y = 0.5x². If the component of velocity along the x axis is vx = (5t) ft/s, where t is in seconds, determine the particle's distance from the origin O and the magnitude of its acceleration when t = 1s. When t = 0, x = 0, y = 0. -y =
A particle moves along the curve y = x - (x2/400), where x and y are in ft. If the velocity component in the x direction is vx = 2 ft/s and remains constant, determine the magnitudes of the velocity and acceleration when x = 20 ft.
The motorcycle travels with constant speed v0 along the path that, for a short distance, takes the form of a sine curve. Determine the x and y components of its velocity at any instant on the curve. y C -L- - y = c sin (7x) -L C X
The roller coaster car travels down the helical path at constant speed such that the parametric equations that define its position are x = c sin kt, y = c cos kt, z = h − bt, where c, h, and b are constants. Determine the magnitudes of its velocity and acceleration. Х 2 - У
Show that if a projectile is fired at an angle from the horizontal with an initial velocity v0, the maximum rangethe projectile can travel is given by Rmax = v02/g, where g isthe acceleration of gravity. What is the angle for thiscondition?
Pegs A and B are restricted to move in the elliptical slots due to the motion of the slotted link. If the link moves with a constant speed of 10 m/s, determine the magnitudes of the velocity and acceleration of peg A when x = 1 m. 류 + y2 = 1 y B D 고 v = 10 m/s X
The van travels over the hill described by y = (-1.5(10-³) x² +15) ft. If it has a constant speed of75 ft/s, determine the x and y components of the van'svelocity and acceleration when x = 50ft. 15 ft y y = (-1.5 (10-³) x² +15) ft -100 ft-
The flight path of the helicopter as it takes off from A is defined by the parametric equations x = (2t²) m and y = (0.04t³) m, where t is the time in seconds. Determine the distance the helicopter is from point A and the magnitudes of its velocity and acceleration when t = 10 s. y Al X
Determine the minimum initial velocity v0 and the corresponding angle θ0 at which the ball must be kicked in order for it to just cross over the 3-m-high fence. 6 m 3 m
The catapult is used to launch a ball such that it strikes the wall of the building at the maximum height of its trajectory. If it takes 1.5 s to travel from A to B, determine the velocity vA at which it was launched, the angle of release θ, and the height h. 3.5 ft A 0 18 ft h
Neglecting the size of the ball, determine the magnitude vA of the basketball’s initial velocity and its velocity when it passes through the basket. 30% A 2 m -10 m- B ww 3 m
Show that the girl at A can throw the ball to the boy at B by launching it at equal angles measured up or down from a 45° inclination. If vA = 10 m/s, determine the range R if this value is 15°, i.e., θ₁ = 45° -15° = 30° and θ₂ =45° +15° = 60°. Assume the ball is caught at the same
The girl at A can throw a ball at vA= 10 m/s. Calculate themaximum possible range R = Rmax and the associated angle θ at which it should be thrown. Assume the ball is caught at B at the same elevation from which it is thrown. VA = 10 m/s A -R B
The ball at A is kicked with a speed vA = 16 ft/s and at an angle θA = 30°. Determine the point (x, –y) where it strikes the ground. Assume the ground has the shape of a parabola as shown. ·X B X y = -0.04x²
The ball at A is kicked such that θA = 30°. If it strikes the ground at B having coordinates x = 15 ft, y = -9 ft, determine the speed at which it is kicked and the speed at which it strikes the ground. y X B X y = -0.04x²
A golf ball is struck with a velocity of 80 ft/s as shown. Determine the speed at which it strikes the ground at B and the time of flight from A to B. VA = 80 ft/s 45° 10⁰ -d- B
A golf ball is struck with a velocity of 80 ft/s as shown. Determine the distance d to where it will land. VA = 80 ft/s 45° 10° -d- B
The pitching machine is adjusted so that the baseball is launched with a speed of vA = 30 m/s. If the ball strikes the ground at B, determine the two possible angles θA at which it was launched. 1.2 m VA = 30 m/s TOA -30 m- B
The firefighter at A uses the hose which ejects a steady stream of water at 10 m/s. Calculate the maximum range R = Rmax to which the water particles can be “thrown” and the angle θ at which he must hold the nozzle. A 10 m/s R- B
Show that the firefighter at A can "throw" water particles on B by aiming the nozzle at equal angles, measured up at θ₁ = 45° -15° = 30° and θ₂ = 45° +15° = 60°. The water has a speed of 10 m/s at the nozzle. A 10 m/s -R- B
The skateboard rider leaves the ramp at A with an initial velocity vA at a 30° angle. If he strikes the ground at B determine vA and the time of flight. A VA 1 m 30⁰ -5 m- B
A projectile is fired from the platform at B. The shooter fires his gun from point A at an angle of 30°. Determine the muzzle speed of the bullet if it hits the projectile at C. B XXXXX - A 30° [1.8 m -20 m C 10 m
If the motorcycle leaves ramp A traveling at 110 ft/s, determine the height h ramp B must have so that the motorcycle lands safely. A 110 ft/s 30⁰ [30 ft -350 ft- B
The drinking fountain is designed such that the nozzle is located a distance away from the edge of the basin as shown. Determine the maximum and minimum speed at which water can be ejected from the nozzle so that it does not splash over the sides of the basin at B and C. 50 mm A 40° B 100 mm - 250
The hose is held at an angle θ = 30° with the horizontal, and the water is discharged at A with a speed of vA = 40ft/s. If the water stream strikes the building at B, determine the two possible distances s from the building. VA = 40 ft/s A 0 4 ft S- B 8 ft
Water is discharged from the hose with a speed of 40 ft/s. Determine the two possible angles u the firefighter can hold the hose so that the water strikes the building at B. Take s = 20 ft. VA = 40 ft/s A 8 4 ft B 8 ft
The man stands 60 ft from the wall and throws a ball at it with a speed of v0 = 50 ft/s. Determine the angle θ at which he should release the ball so that it strikes the wall at the highest point possible. What is this height? The room has a ceiling height of 20 ft. % = 50 ft/s 5 ft - 60 ft- 20 ft
The velocity of the water jet discharging from an orifice can be obtained from v = √2 gh, where h = 2 m is the depth of the orifice from the free water surface. Determine the time for a particle of water leaving the orifice to reach a point B and the horizontal distance x where it hits the
The snowmobile is traveling at 10 m/s when it leaves the embankment at A. Determine the time of flight from A to B and the range R of the trajectory. A 40° 3 نیا -R- 5 4 B
The firefighter wishes to direct the flow of water from his hose to the fire at B. Determine two possible angles θ₁ andθ2 at which this can be done. Water flows from the hose at vA = 80 ft/s. 0 -35 ft B 20 ft
The buckets on the conveyor travel with a speed of 15 ft/s. Each bucket contains a block which falls out of the bucket when θ = 120°. Determine the distance s to where the block strikes the conveyor. Neglect the size of the block. 0 = 120⁰ 1 ft 3 ft
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. y A -400 m- B y = 200 e 1000 23 x
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) y = 20(10³) X P x (mm)
The catapult is used to launch a ball such that it strikes the wall of the building at the maximum height of its trajectory. If it takes 1.5 s to travel from A to B, determine the velocity vA at which it was launched, the angle of release θ and the height h. 3.5 ft To - 18 ft. B
When the car reaches point A it has a speed of 25 m/s. If the brakes are applied, its speed is reduced byDetermine the magnitude of acceleration of the car just before it reaches point C. a₁ = (-1/t¹²) m/s². at 4
When the car reaches point A, it has a speed of 25 m/s. If the brakes are applied, its speed is reduced by at = (0.001s - 1) m/s2. Determine the magnitude of acceleration of the car just before it reaches point C. p = 250 m B 30° -200 m- A
Starting from rest, the motorboat travels around the circular path, ρ = 50 m, at a speed v = (0.8t) m/s, where t is in seconds. Determine the magnitudes of the boat’s velocity and acceleration when it has traveled 20 m. p = 50 m
The automobile has a speed of 80 ft/s at point A and an acceleration a having a magnitude of 10 ft/s2, acting in the direction shown. Determine the radius of curvature of the path at point A and the tangential component of acceleration. A 0 = 30° a n
A train travels along a circular track having a radius of 2000 ft. If the speed of the train is uniformly increased from 6 mi/h to 8 mi/h in 1 min, determine the magnitude of the acceleration when the speed of the train is 7 mi/h. 1 mi = 5280 ft.
A boat has an initial speed of 16 ft/s. If it then increases its speed along a circular path of radius ρ = 80 ft at the rate of v̇ = (1.5s) ft/s2, where s is in feet, determine the normal and tangential components of the boat’s acceleration at s = 16 ft.
The car passes point A with a speed of 25 m/s after which its speed is defined by v = (25-0.15s) m/s, where s is in meters. Determine the magnitude of the car's acceleration when it reaches point B, where s = 51.5 m and x = 50 m. 16 m -y = 16 B 1 625 A X
A particle moves along the curve y = 1 + cos x with a constant speed v = 4 ft/s. Determine the normal and tangential components of its velocity and acceleration at any instant.
Starting from rest, the motorboat travels around the circular path, ρ = 50 m, at a speed v = (0.2t2) m/s, where t is in seconds. Determine the magnitudes of the boat’s velocity and acceleration at the instant t = 3 s. p = 50 m + V
The position of a particle is defined by r = {4(t - sin t)i + (2t2 - 3)j} m, where t is in seconds and the argument for the sine is in radians. Determine the speed of the particle and its normal and tangential components of acceleration when t = 1 s.
The satellite S travels around the earth in a circular path with a constant speed of 20 Mm/h. If the acceleration is 2.5 m/s2 determine the altitude h. Assume the earth’s diameter to be 12 713 km. S.
The motorcycle travels up the hill at a constant speed of 15 m/s. Determine the magnitude of its acceleration as a function of x. y -X- y= 1 x² 1000 -X
The motorcyclist travels along the curve at a constant speed of 30 ft/s. Determine his acceleration when he is located at point A. Neglect the size of the motorcycle and rider for the calculation. y y = 500 X -100 ft v = 30 ft/s A X
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