Max Height & Velocity of a Vertical Ball: Calculus Math Problem Solution

[jendoley]

If a ball is thrown vertically upward with a velocity of 72 ft/s, then its height after t seconds is s(t)=64t-16t^2.

1. What is the maximum height reached by the ball? Explain why this location is the maximum using the derivative as part of your answer.
2. find the velocity of the ball right as it hits the ground (do not assume it is zero). Explain your answer.

I have no attempt on this problem. Not sure where to start.

 

[Ouabache]

Welcome jendoley to Physics Forums ! You will find there are many interesting topics
and threads to see here. For questions like yours,
I would start by posting in a section with questions of similar type. for example:
physicsforums> homework and coursework questions> calculus and beyond.
(i will request to have your thread moved there)

Also you ought to read the first persistent thread there, titled: "FAQ Why Hasn't Anybody Answered my Question?" It gives important information the poster should be aware of.

If you have had some physics, it would give you good insight to read up on 'projectile motion'.

 

[Dembadon]

If a ball is thrown vertically upward with a velocity of 72 ft/s, then its height after t seconds is s(t)=64t-16t^2.

1. What is the maximum height reached by the ball? Explain why this location is the maximum using the derivative as part of your answer.
2. find the velocity of the ball right as it hits the ground (do not assume it is zero). Explain your answer.

I have no attempt on this problem. Not sure where to start.

In addition to Ouabache's advice, hopefully these questions will help you find your way to the answer and understand how you got there.

1) Do you remember how to find extrema on an interval? If the derivative of a function is the slope of the tangent line at a given point on the curve, what would you need to set the derivative equal to in order to represent a line with a slope of zero? Why does the tangent line need to have a slope of zero?

It might help to draw a picture of your function on a coordinate plane.

2) What are the known values and unknown values. (make a list of initial and final values)