explain [14) A student throws a projectile horizontally at a target a horizontal distance R away. The projectile is released from height H above the ground and strikes the target a height h below the release point, as shown above. Which of the following indicates the values that must be known for a student to calculate the initial speed of the projectile? -R (A) R only (B) H only (C) H and R only DJ h and R only (E) H, h and R [15] An airplane travels horizontally at a constant velocity . An object is dropped from the plane, and one second later another object is dropped from the plane. If air resistance is negligible, what happens to the vertical distance between the two objects while they are both falling? A B [A) It increases. [B) It decreases. C) It remains the same. (D) It depends on the mass of the objects. E) It depends on the horizontal speed of the plane. [16] Two stones, represented in the figure above, are thrown from the same height with the same initial speed. Stone A is thrown vertically downward and stone B is thrown horizontally. If the stones are thrown at the same time and air resistance is negligible, which of the following is true? [A) The two stones will reach the ground at the same time with the same speed. [B) The two stones will reach the ground at the same time but with different speeds. C) Stone will reach the ground first, but stone will have the greater speed just before hitting the ground. [D) Stone A will reach the ground first, but the two stones will have the same speed just before they hit the ground. (E) Stone will reach the ground first, and will have the greater speed just before hitting the ground. Page 9 of 11 C. Projectile Launched at an angle (17) A projectile is launched from the ground with an initial velocity of 12 m/s at an angle of 30" above the horizontal. The projectile lands on a hill 7.5 m away. The height at which the projectile lands is most nearly 1.78 m (18) A projectile is launched with a speed of 40 m/s at an angle of 30 above the horizontal, as shown in the figure below. The projectile lands on a plateau 3 s later. The height Ay of the plateau is most nearly 40 m/s 30 15 m (19) A projectile is launched with a speed of 30 m/'s at an angle of 600 above the horizontal. The projectile lands on a ledge that is 15 m above the launch point, as shown. The horizontal and vertical components v, and v,, respectively, of the velocity when the projectile lands are 30 60 15 m V's = 15 m/s vy= - 19.5 m/s (20) A projectile is launched from the top of a 15 m tall building at a speed of 25 my's at an angle of 50 above the horizontal. The horizontal distance from the base of the building to where the projectile lands is most nearly 73. 9 m (21) A spring-loaded gun can fire a projectile to a height h if it is fired straight up. If the same gun is pointed at an angle of 45 from the vertical, what maximum height can now be reached by the projectile? 2 (22) A cannonball is shot from the top of a 30 m high hill at a velocity of 25 m/s and at an angle of 40* above the horizontal and lands on the ground below. The speed of the cannonball at the top of its path is most nearly (A) 0 (B) 16 m/s (C] 19 m/s (D) 25 m/: (E] 29 m/s Page 10 of 11(23) A projectile is launched from level ground with an initial speed v0 at an angle 9 with the horizontal. Ifair resistance is negligible. how long will the projectile remain in the air? (A) Zvo/y (B) Zvo case/g (C) v0 case/g (D) v0 sine/g (E) Zvo sine/g (24) Pairs of students stand in two rows separated by four meters and face each other. Each pair of students has a large ball. The students pass the balls from their chest to their partners' chest. as shown. A video camera is used to lm this interaction. When viewing the video, the students note that the highest point in the trajectories of all the balls are nearly the same height above the ground. Which of the following claims is supported by this evidence? (A) The students threw the ball to their partner with nearly the same speed. (B) The students threw the ball to their partner at nearly the same angle to the horizontal. [C] The time the ball is in the air is nearly the same for each ball. (D )lt is impossible for the balls to not go to the same height. because the distance between each pair of students is the same. (E) Each ball must have the same mass. (6] A student throws a metal sphere, which follows the path shown above. If air resistance is negligible, which of the following is a correct relationship between the magnitudes of the accelerations ak, al , and aM at the three points shown? (A) OK=aL=OM (B) ak=GL>GM [C] OK=aMeal [D) axzal,=M [E] aRzaMxa (7 ]The velocity of a projectile at launch has a horizontal component vh and a vertical component vy. Air resistance is negligible. When the projectile is at the highest point of its trajectory, which of the following show the vertical and horizontal components of its velocity and the vertical component of its acceleration? Vertical Velocity Horizontal Acceleration Velocity A. VV B. WV D. VH (8] A ball is kicked from the ground with an initial speed vo at an angle e above the horizontal. Which of the following best describes the magnitudes of the velocity and acceleration of the ball when it reaches the highest point of its trajectory? Velocity Acceleration A. 0 B. VoCOSO C. vosine D. VoCOSB 9.8 m/sz v.sing 9.8 m/s2 (9] Two projectiles are launched with the same initial speed from the same location, one at a 30* angle and the other at a 60* angle with the horizontal. They land at the same height at which they were launched. If air resistance is negligible, how do the projectiles' respective maximum heights, #30 and H60. and times in the air, 730 and 760, compare with each other? Maximum Height Time in Air H30