A ball is thrown upwards from the roof of a school, 16m high, with an initial velocity of 20m/s. The height of the ball above the ground at time t is given by the function h(t) = 4.9t^2 + 20t + 16, t=0.

A) What is the maximum height of the ball?

B) How fast was the ball travelling when it hit the ground?

Question

A ball is thrown upwards from the roof of a school, 16m high, with an initial velocity of 20m/s. The height of the ball above the ground at time t is given by the function h(t) = 4.9t^2 + 20t + 16, t>=0.
 
A) What is the maximum height of the ball?

B) How fast was the ball travelling when it hit the ground?

anonymous · Answer

calculus and vectors

anonymous · Answer

yeah lol

anonymous · Answer

So you want to find the local maximum of the function h(t). Do you know how to start off?

anonymous · Answer

I was thinking of finding the derivative of the given function and setting it to 0.

anonymous · Answer

Yep :) and that will give you your critical points which then, by using the second derivative would allow you to see if that point(s) is a maximum or minimum.

anonymous · Answer

awesome. could you lend a hand on b)? :D

anonymous · Answer

find the value t at which the ball hits the ground (so h(t) = 0) and plug in the value t into your velocity function (which is h'(t))

anonymous · Answer

thank you so much! you were great help.

anonymous · Answer

No problem :)