Question

A soccer ball is kicked from the ground with an initial upward velocity of 90 feet per second. The equation h=-16t^2+90t gives the height h of the ball after t seconds. Find the maximum height of the ball.

Answer 1

Answer:

$h_{max} = 30.012\,ft$

Step-by-step explanation:

The maximum height of the soccer can be determined with the help of the First Derivative and Second Derivative Tests, whose expression are introduced below:

$\frac{dh}{dt} = -32\cdot t + 90$

$-32\cdot t + 90 = 0$

$t = 0.356\,s$

$\frac{d^{2}h}{dt^{2}} = -32$

According to both tests, the critical value leads to maximum height. Then:

$h_{max} = -16\cdot (0.356)^{2}+90\cdot (0.356)$

$h_{max} = 30.012\,ft$