# Calculus Velocity and Acceleration Problem.

Okay so this is the problem: "On a certain planet, a ball is thrown upward with a speed of 33 feet per second from the edge of a cliff 44 feet above the ground. When does it hit the ground? (use a(t) = −22).

I already know that the answer is 4 seconds but I don't understand how to get there. Can someone please guide me and explain to me the process of solving this problem? Thank you!

Hint: Start with the fact that acceleration is the derivative of velocity, which is the derivative of position. We know that $a(t) = -22$, so integrate it to find the velocity, using the information about the initial velocity in order to find the constant of integration. Then once you've found the velocity $v(t)$, you can integrate that to find the position, and again you'll have a new constant of integration that you can find the value of by using the information about the original position. Once you've found the position $x(t)$, you can solve for the time $t$ where the position of the ball is at the ground, i.e. $x = 0$.
• @Dylan Yes it would, because when you integrate you get $v(t) = -22t + C$, and then you use the fact that $v(0) = 33$ to solve for $C$, and you get $C=33$. Commented Apr 23, 2014 at 23:38