Question

question 10 (1 point)
john and peter stand on a snow - covered roof. they both throw snowballs with the same initial speed, but in different directions. john throws his snowball downward, at 30° below the horizontal; peter throws his snowball upward, at 30° above the horizontal. which of the following statements are true about just before the snowballs reach the ground below? (there could be more than one correct choice.)
□ a) johns snowball will stay in the air longer than peters snowball.
□ b) peters snowball will stay in the air longer than johns snowball.
□ c) peters snowball has exactly the same acceleration as johns snowball.
□ d) johns snowball has a greater downward acceleration than peters snowball.

Explanation:

Step1: Analyze the time - of - flight

Peter's snowball has an initial upward vertical velocity component (\(v_{0y}=v_0\sin30^{\circ}\)), so it will first go up, then come back to the level of the roof (taking some time), and then fall to the ground. John's snowball has an initial downward vertical velocity component (\(v_{0y}=v_0\sin30^{\circ}\)), so it will take less time to reach the ground.

Step2: Analyze the acceleration

The only force acting on each snowball is gravity (neglecting air - resistance). According to Newton's second law \(F = ma\), and \(F=mg\), so \(a = g\) for both snowballs. The acceleration of an object in free - fall (neglecting air resistance) is \(a=-g=- 9.8\ m/s^{2}\) (taking downwards as negative) for both snowballs.

Answer:

B. Peter's snowball will stay in the air longer than John's snowball; C. Peter's snowball has exactly the same acceleration as John's snowball.