How to find speed of the ball?

Question

A ball is thrown upward with a speed of 40 feet per second from the edge of a cliff 500 feet above the ground. What is the speed of the ball when it hits the ground? Use acceleration due to gravity as -32 feet per second squared and approximate your answer to 3 decimal places.

Answer 1

Here's how I would do it.

step 1: Derive a formula for speed as a function of what you know: acceleration due to gravity (g) and distance (d).

We know that for vertical fall, d = 0.5*g*t^2. Furthermore, v(t) = gt. Thus, from these two equations,

v = sqrt(2gd).

step 2: Find total free-fall distance of the ball from the top of its flight to the ground. Using the formula

40 = sqrt(2gh) which implies that the max height (h) of the ball is 40²/(2g). Then, the total distance of free-fall is d = 500 + 40²/(2g). Now, you can calculate v!

Best.