Question

24. A stone thrown vertically up from the top of a tower with a velocity 20m/s reaches the ground in 6 seconds. Find the height of the tower. [56.4 m] 25. A particle is projected vertically up from the foot of the tower 392 m high with velocity 98 m/s. At the same instant another body is dropped from the top. Find when and where they will meet. [t=4 seconds; h=313.6 m above the foot of the tower] 26. A ball is thrown vertically up with a speed of 14 m/s. 2 s later a second ball is dropped from the same point. Find when and where the two balls will meet. [t=3.5 s; h=11 m] 27. A particle moves in the xy plane such that, at time t, its displacement from a fixed point O is given by r = 4ti + (3t?5t²)j. Find the velocity vector at time t and hence find the velocity components when t=0. Show that the acceleration is constant. Do you notice anything significant about this acceleration? [v = 4i + 3j] 28. A short fired horizontally from the top of a tower 176.4 m high hits the ground at a distance 1200 m from the foot of the tower. Find the velocity of projection. [200 m/s] 29. A short is fired from a gun on the top of a hill 90 m high with velocity 80 m/s at an angle 30° with the horizontal. Find its horizontal distance from the point of projection when it strikes the ground. [400?3 m] 30. You throw a rock off the cliff at 10 m/s, 20° above the horizontal. The cliff is 25 m high. With what angle does it the rock hit the ground? [67.2°] 31. You ride your bike over a ramp. The ramp is slanted at 28°. You land 12 meters away. What was your velocity as you rode off the ramp? [11.9 m/s] 32. A projectile is launched on level ground. At the peak of its trajectory, it is 7.5 m high. It lands 10 m from where it was launched. At what angle was the projectile launched? [71.6°] 33. A stone is thrown off a cliff. It hits the ground with an angle of 73.4° and a speed of 65.7 m/s. If the cliff is 200 m high, how fast was the stone initially thrown? [20.1 m/s] 34. Prove that the time of flight T and the horizontal range R of a projectile are connected by the equation gT² = 2R tan ? 35. Figure (not drawn to scale) 3.12 shows a fighter plane that has a speed v? of 300 km/h, flying at an angle ? =15? below the horizontal when a decoy rocket is released. The horizontal distance between the release point and the point where the decoy strikes the ground is x =600 m. Take g = 10 m/s². (a) How long was the decoy in the air? (b) How high was the plane when the decoy was released? [(a) 7.45 s, (b) 438.2m] Figure 3.12 See exercise 35

          24. A stone thrown vertically up from the top of a tower with a velocity 20m/s reaches the ground in 6 seconds. Find the height of the tower. [56.4 m]
25. A particle is projected vertically up from the foot of the tower 392 m high with velocity 98 m/s. At the same instant another body is dropped from the top. Find when and where they will meet. [t=4 seconds; h=313.6 m above the foot of the tower]
26. A ball is thrown vertically up with a speed of 14 m/s. 2 s later a second ball is dropped from the same point. Find when and where the two balls will meet. [t=3.5 s; h=11 m]
27. A particle moves in the xy plane such that, at time t, its displacement from a fixed point O is given by r = 4ti + (3t?5t²)j. Find the velocity vector at time t and hence find the velocity components when t=0. Show that the acceleration is constant. Do you notice anything significant about this acceleration? [v = 4i + 3j]
28. A short fired horizontally from the top of a tower 176.4 m high hits the ground at a distance 1200 m from the foot of the tower. Find the velocity of projection. [200 m/s]
29. A short is fired from a gun on the top of a hill 90 m high with velocity 80 m/s at an angle 30° with the horizontal. Find its horizontal distance from the point of projection when it strikes the ground. [400?3 m]
30. You throw a rock off the cliff at 10 m/s, 20° above the horizontal. The cliff is 25 m high. With what angle does it the rock hit the ground? [67.2°]
31. You ride your bike over a ramp. The ramp is slanted at 28°. You land 12 meters away. What was your velocity as you rode off the ramp? [11.9 m/s]
32. A projectile is launched on level ground. At the peak of its trajectory, it is 7.5 m high. It lands 10 m from where it was launched. At what angle was the projectile launched? [71.6°]
33. A stone is thrown off a cliff. It hits the ground with an angle of 73.4° and a speed of 65.7 m/s. If the cliff is 200 m high, how fast was the stone initially thrown? [20.1 m/s]
34. Prove that the time of flight T and the horizontal range R of a projectile are connected by the equation gT² = 2R tan ?
35. Figure (not drawn to scale) 3.12 shows a fighter plane that has a speed v? of 300 km/h, flying at an angle ? =15? below the horizontal when a decoy rocket is released. The horizontal distance between the release point and the point where the decoy strikes the ground is x =600 m. Take g = 10 m/s².
(a) How long was the decoy in the air?
(b) How high was the plane when the decoy was released? [(a) 7.45 s, (b) 438.2m]
Figure 3.12 See exercise 35

24. A stone thrown vertically up from the top of a tower with a velocity 20m/s reaches the ground in 6 seconds. Find the height of the tower. [56.4 m]
25. A particle is projected vertically up from the foot of the tower 392 m high with velocity 98 m/s. At the same instant another body is dropped from the top. Find when and where they will meet. [t=4 seconds; h=313.6 m above the foot of the tower]
26. A ball is thrown vertically up with a speed of 14 m/s. 2 s later a second ball is dropped from the same point. Find when and where the two balls will meet. [t=3.5 s; h=11 m]
27. A particle moves in the xy plane such that, at time t, its displacement from a fixed point O is given by r = 4ti + (3t?5t²)j. Find the velocity vector at time t and hence find the velocity components when t=0. Show that the acceleration is constant. Do you notice anything significant about this acceleration? [v = 4i + 3j]
28. A short fired horizontally from the top of a tower 176.4 m high hits the ground at a distance 1200 m from the foot of the tower. Find the velocity of projection. [200 m/s]
29. A short is fired from a gun on the top of a hill 90 m high with velocity 80 m/s at an angle 30° with the horizontal. Find its horizontal distance from the point of projection when it strikes the ground. [400?3 m]
30. You throw a rock off the cliff at 10 m/s, 20° above the horizontal. The cliff is 25 m high. With what angle does it the rock hit the ground? [67.2°]
31. You ride your bike over a ramp. The ramp is slanted at 28°. You land 12 meters away. What was your velocity as you rode off the ramp? [11.9 m/s]
32. A projectile is launched on level ground. At the peak of its trajectory, it is 7.5 m high. It lands 10 m from where it was launched. At what angle was the projectile launched? [71.6°]
33. A stone is thrown off a cliff. It hits the ground with an angle of 73.4° and a speed of 65.7 m/s. If the cliff is 200 m high, how fast was the stone initially thrown? [20.1 m/s]
34. Prove that the time of flight T and the horizontal range R of a projectile are connected by the equation gT² = 2R tan ?
35. Figure (not drawn to scale) 3.12 shows a fighter plane that has a speed v? of 300 km/h, flying at an angle ? =15? below the horizontal when a decoy rocket is released. The horizontal distance between the release point and the point where the decoy strikes the ground is x =600 m. Take g = 10 m/s².
(a) How long was the decoy in the air?
(b) How high was the plane when the decoy was released? [(a) 7.45 s, (b) 438.2m]
Figure 3.12 See exercise 35

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