Chapter 8, Problem 3P

The height in the vertical plane of a ball thrown from the ground with an initial velocity of $v\left(0\right)=250\text{m/s}$ satisfies the relationship

$y\left(t\right)=v\left(0\right)t-\frac{1}{2}g{t}^2\text{m}$.

Find the following:

(a) Write the quadratic equation for the height $y\left(t\right)$ of the hail.

(b) The velocity $v\left(t\right)=\frac{dy\left(t\right)}{dt}$.

(e) The acceleration $a\left(t\right)=\frac{dv\left(t\right)}{dt}=\frac{d^{2}y\left(t\right)}{d{t}^2}$.

(d) The time required to reach the maximum height, as well as the corresponding height $y_{\max }$. Use your results to sketch $y\left(t\right)$.