Question

Suppose you look out the window of a skyscraper and see someone throw a tomato downward from above your window. your window is at a height of 450 feet above the ground. the tomato passes your window after 2 seconds and hits the ground 5 seconds after it was thrown. neglect air resistance, and give units in your answers. (a) find the velocity (with the positive direction pointing up) at which the tomato was thrown.

Answer 1

Formula for height
r(t) = a/2 t² + v₀ t + r₀
where
a = acceleration = -32 ft/sec² (gravity)
v₀ = initial velocity
r₀ = initial height
r(t) = -16t² + v₀ t + r₀
Tomato passes window (height = 450 ft) after 2 seconds:
r(2) = 450
-16(4) + v₀ (2) + r₀ = 450
r₀ = 450 + 64 - 2v₀
r₀ = 514 - 2v₀
Tomato hits the ground (height = 0 ft) after 5 seconds:
r(5) = 0
-16(25) + v₀ (5) + r₀ = 0
r₀ = 16(25) - 5v₀
r₀ = 400 - 5v₀

r₀ = 514 - 2v₀ and r₀ = 400 - 5v₀
514 - 2v₀ = 400 - 5v₀
5v₀ - 2v₀ = 400 - 514
3v₀ = −114
v₀ = −38
Initial velocity = −38 ft/sec (so tomato was thrown down)
(initial height = 590 ft)