A cannonball was launched by a cannon. The function H(t)=−t2+100t+100 describes the position of the cannonball t seconds after it was launched and the height H is in metres. How long did it take for the cannonball to reach its maximum height?

The answer to your question is t = 50 s

Explanation:

Data

Function

H(t) = -t² + 100t + 100

Process

1.- Find the derivative of the function to get the maximum

H'(t) = -2t + 100

2.- Equal to zero the derivative

          -2t + 100 = 0

3.- Solve for t

          -2t = -100

             t = -100/-2

             t = 50 s

4.- Conclusion

It takes 50 s to reach the maximum height