Chapter 4.8, Problem 16P

To determine

To find how high will it go? When will it return to the ground?

Answer to Problem 16P

The ball will go high at 100 feet and it will return to the ground in 5 seconds.

Explanation of Solution

Given information: A ball is thrown directly upward with an Initial speed of $80ft/s$ .

Calculation: The required solution is obtained as,

Use the projectile equation, $h=vt-16t^2$ .

When $h=0$ the projectile return to the ground. Solve for t.

  $\begin{array}{l}h=vt-16t^2\\ 0=80t-16t^2\\ 16t^2-80t=0\\ 16t\left(t-5\right)=0\\ t=0,5\end{array}$

Take $t=5$ sec.

Find the maximum height by substituting $t=2.5$ seconds into the equations.

  $\begin{array}{l}h=vt-4.9t^2\\ h=80\left(2.5\right)-16{\left(2.5\right)}^2\\ h=100\end{array}$

Hence, the ball will go high at 100 feet and it will return to the ground in 5 seconds.