Question

A ball thrown horizontally from the top of a building hits the ground in 0.600 s. If it had been thrown with twice the speed in the same direction, it would have hit the ground in:________.

a. 4.0 s.
b. 1.0 s.
c. 0.50 s.
d. 0.25 s.
e. 0.125 s.

Answer 1

none of the answers is correct, the time is the same t₁ = t₂ = 0.600 s

Step-by-step explanation:

This is a kinematics exercise, analyze the situation a bit. The vertical speed in both cases is the same is zero, the horizontal speed in the second case is double (vₓ₂ = 2 vₓ₁)

let's find the time to hit the ground

y = y₀ + I go t - ½ g t²

0 = y₀ - ½ g t²

t = √ 2y₀ / g

with the data from the first launch

y₀i = ½ g t²

y₀ = ½ 9.8 0.6²

y₀ = 1,764 m

with this is the same height the time to descend in the second case is the same

t₂ = 0.600 s

this is because the horizontal velocity change changes the offset on the x axis, but does not affect the offset on the y axis

Therefore, none of the answers is correct, the time is the same

t₁ = t₂ = 0.600 s