Problem Set question

Question

Calculus is a powerful tool used in all areas of physics. One of the initial applications areas is classical physics, particularly Newtonian mechanics. An important function is the position function s(t) that measures how far the object is from point 00 at time tt. The question below deals with just the position function s(t).

 

Problem Set question:

 

The position function for a falling objects is given by s(t)=−16t2+v0t+s0, where s(t) is the height of the object in feet, v0 is the initial velocity, s0s0 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 75 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 .

 

Answer 1

At maximum height, velocity (ds/dt) will be zero.

This is a typical maximum problem and as usual the maximum will be found when the derivative is 0!

Differentiate s(t) with respect to t and set the derivative=0; then solve for t.

The plug your answer into s(t) to get the maximum height.