Introduction to Calculus in Physics

Question

Problem Set question:

 

The position function for a falling objects is given by s(t)=−16t^2+v0t+s0, where s(t) is the height of the object in feet, v0 is the initial velocity, s0 is the initial height, and t is the time in seconds.

 

A ball is shot upwards from the surface of the earth (s0=0) with an initial velocity of 55 feet per second. What is the maximum height reached by the ball?

 

Round your answer to the nearest integer.

 

The maximum height reached by the ball is 

______(units)

Answer 1

At the maximum height the velocity is instantaneously zero

v(t) = s'(t) = 0

s'(t) = -32t + v0

v0 = 55

so find t when s'(t) = 0

then substitute this into s(t) to find the maximum height