Question

CP Bang! A student sits atop a platform a distance h above the ground. He throws a large firecracker horizontally with a speed. However, a wind blowing parallel to the ground gives the firecracker a constant horizontal acceleration with magnitude a. As a result, the firecracker reaches the ground directly below the student. Determine the height h in terms of v, a, and g. Ignore the effect of air resistance on the vertical motion.

Answer 1

h = v₀ g / a

Step-by-step explanation:

We can solve this problem using the kinematic equations. As they indicate that the air does not influence the vertical movement, we can find the time it takes for the body to reach the floor

y =
`v_(oy)` t - ½ g t²

The vertical start speed is zero

t² = 2t / g

The horizontal document has an acceleration, with direction opposite to the speed therefore it is negative, the expression is

x = v₀ₓ t - ½ a t²

Indicates that it reaches the same exit point x = 0

v₀ₓ t = ½ a t2

v₀ₓ = ½ a (2h / g)

v₀ₓ = v₀

h = v₀ g / a