The equation for free fall at the surface of Planet X is s = 4.31t2 with t in seconds. Assume a rock is dropped from the top of a 600m cliff. Find the speed of the rock at t = 3 sec

Question

The equation for free fall at the surface of Planet X is s = 4.31t² with t in seconds. Assume a rock is dropped from the top of a  600m cliff. Find the speed of the rock at t = 3 sec

MULTIPLE CHOICE

26.86 m/sec

12.93 m/sec

11.93 m/sec

25.86 m/sec

Answer 1

We know the rock is falling for 3 seconds, so t = 3 seconds

We can calculate the distance it traveled using the equation s = 4.31t²|_t=3

Therefore, s = 4.31(3²) = 38.79 meters

We have v₀ = 0m/s since the rock is dropped

Now we have to find v_f

First, we'll find the acceleration though.

We need an equation that has a, v₀, t, and s in it with s being the distance.

We'll use the equation s = 1/2 at² + v₀t

v₀ is 0, so that last term cancels

Our equation becomes s = 1/2 at².

We can plug in and solve for the acceleration, but notice that this equation looks like the equation for s they gave us: s = 4.31t²

The 4.31 in that equation is the 1/2 a.

Therefore, a = 8.62.

Usually, the acceleration is just twice the number in front of the t².

Now calculate v_f using the equation a = (v_f - v₀)/ t or the equation v_f = at + v₀