Question

You are standing on top of a 10-m high cliff. Below you, on the ground, is a circular target with a radius of 0.5 meters, whose center is 5 meters from the base of the cliff. On top of the cliff, and at the edge, is a circular track of radius r. You are going to drop a 5-kg ball from a height h above the cliff onto the ramp, so that the ball travels around the track and is shot off from the top of the track traveling horizontally. (The track is 3/4 of a circle).

(a) Ignoring the radius of the circular track, from what height h, above the cliff, should you drop the ball so that it hits the center of the target? Ignore air resistance.

(b) You are going to repeat this experiment, but now there is a strong breeze blowing towards the cliff, which will act on the ball with a constant horizontal force of 10 N once it is shot from the cliff. i. If you drop the ball from the same height as in part (a), will you still hit the target? (Anywhere on the target counts, not just the center.) ii. If you want to hit the center of the target, from what height must you now drop the ball? What is the final velocity (magnitude and direction) of the ball, just before it hits the target. iii. Plot the trajectory of the ball.

(c) The wind has died down, and you now want to take into consideration the radius of the circular track. i. If you drop the ball from the same height as calculated in part (a), what can be the maximum radius, r, of the track so that the ball lands anywhere on the target, (not just in the center)? ii. Assuming that the track has the maximum radius calculate in the previous part, what is the centripetal force on the ball when it is at the bottom of the circular track?

Answer 1