Question

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Two tennis ball launchers shoot balls at the same time, angle and initial speed from different floors of a tall building. The balls land in the street below. Ignore air resistance.

Answer 1

1) In a projectile motion, we know that the x-component of the velocity is constant, while the y-component will be accelerated:
v_y = v₀ · sinα + a·t

The ball A will fly for a longer time than ball B because it is launched from a higher place, therefore it will be subject to acceleration for a longer time, resulting in a greater final velocity.

2) Since the x-component of the velocity is constant, the total distance traveled horizontally is:
s = v₀ · cosα · t
Again, since ball A flies for a longer time than ball B, it will travel furtherer.

3) The maximum height can be calculated by the formula:
h_max = h₀ + (v₀² · sin²α / 2g)

Both balls will reach the same height from the starting point, but since ball A starts from a higher point, it will reach the greatest maximum height.

4) The acceleration the two balls are subject to has x-component null and y-component equal to the gravity acceleration, which is constant. Therefore, the two balls are subject to the same acceleration.