Someone in a car going past you at the speed of 45 m/s drops a small rock from a height of 2.1 m/s

Question

How far from the point of the drop will the rock hit the ground? The acceleration due to gravity is 9.8 m/s. answer in m/s

Answer 1

The trick is to consider what happens in the x-direction separately from what happens in the y-direction.

In the y-direction, this problem is exactly the same as if, as you are standing, you drop a small rock from the height of 2.1 meters. To determine how long it takes to hit the ground, you can use the kinematic equation of motion (for constant acceleration): x = v_it + 1/2at² where "x" is the distance the rock falls, "v_i" is the initial velocity which in this case is zero because the rock was dropped, "t" is the time the rock is in the air, and "a" is the acceleration due to gravity (the problem says to use a = 9.8 m/s²)

x = v_it + 1/2at²

2.1 = (0)t + 1/2(9.8)t²

2.1 = 4.9t²

0.42857 = t²

t = √0.42857 = 0.655 seconds

Now consider the x-direction, The rock is traveling at 45 m/s and does so for the 0.655 seconds so the distance traveled is (45)(0.655) = 29.5 meters