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