Part I. A 58-gram ball is thrown vertically upward at 8 m/sec from the roof of a 60-meter tall building. During its fall, it strikes a balcony located below the roof 4 seconds after it is released. The ball then bounces off the balcony and strikes the ground as shown below. Ignore any effects of air resistance; that is, consider the ball to be in freefall.

 

 

(a) Is the object's acceleration at its maximum height UPWARD, DOWNWARD or ZERO?  Support your choice.

(b) What was the vertical velocity when the ball struck the balcony?

(c) Had the ball been thrown straight downward at 8 m/sec, would it have struck the balcony at the same speed, a smaller speed, or a greater speed? Explain your reasoning.

(d) How high is the balcony above the ground? (small h in the diagram)

Part II. The 58-gram ball then bounces vertically off the balcony at a velocity of 27 m/sec eventually striking the ground at the base of the building.   (e) What impulse did the floor of the balcony deliver to the ball during the ball’s bounce?

(f) How much total mechanical energy (PE and KE) did the ball possess as it started its rebound off the balcony?

(g) How high did it rebound? (h2 in the diagram)

(h) Draw a FBD (free body diagram) of the ball at the apex of its rebound.

(i) How much total time did the ball spend in the air? (Do not worry about the time of impact with the floor of the balcony.)