Constant velocity

Question

A rock is dropped from rest and free falls at 10m/s2. How fast will the rock be moving right before it hit the ground it falls 3.3m? How long does it take for the rock to fall 3.3m.

Answer 1

There are a set of "kinematic equations" that will make this fairly easy that you should have been given. One of them is v_f² = v_i² + 2ax where v_f is the final velocity you are seeking, v_i is the initial velocity which in this case is zero because the rock was dropped "from rest", "a" is the acceleration which you were given as 10 m/s², and "x" is the distance the object falls which you were given as 3.3 m. So:

v_f² = v_i² + 2ax

v_f² = 0² + 2(10)(3.3)

v_f² = 66

√v_f² = √66

v_f = 8.1 m/s

The time it takes can be calculated from another of the kinematic equations. Since we now know the final velocity (before rounding off it was 8.1240384 m/s), we can use v_f = v_i + at. So:

v_f = v_i + at

8.1240384 = 0 + 10t

t = 8.1240384/10

t = 0.81 s