Question

Anyone good with calculus? Please help.

Answer 1

First take a time derivative of a function describing motion,

$\frac{d}{dt}h(t)=\frac{d}{dt}-4.9t^2+19.6t-14.6=-9.8t+19.6$.

Finding the maxima of the function is obtained by determining where the critical points are. You can find the critical points by equating the derivative with 0 and solving for t,

$\frac{d}{dt}h(t)=0$

$-9.8t+19.6=0\implies t=\frac{19.6}{9.8}=\boxed{2}$.

So at 2 seconds the ball peaks in height.

To find out the height feed 2 to the function h.

$h(2)=-4.9\cdot2^2+19.6\cdot2-14.6=\boxed{5}$.

So at 2 seconds the ball reaches maximum height of 5 meters.

Hope this helps :)