Chapter MPS, Problem 5.3MPS

a.

To determine

To find:The time required to hit the ground by the arrow.

Answer to Problem 5.3MPS

The time required to hit the ground by the arrowis $5.38\sec$ .

Explanation of Solution

Given information: The function is $h\left(t\right)=v_{0}t-16t^2+h_0$ .

Calculation:

Consider the function.

  $h\left(t\right)=v_{0}t-16t^2+h_0$

Substitute the values in above equation.

  $\begin{array}{l}0=85t-16t^2+6\\ t=5.38\end{array}$

Thus, the time required to hit the ground by the arrow is $5.38\sec$ .

b.

To determine

To find: The maximum height gained by arrow.

Answer to Problem 5.3MPS

The maximum height gained by arrowis $124.89\text{ft}$ .

Explanation of Solution

Given information: The function is $h\left(t\right)=v_{0}t-16t^2+h_0$ .

Calculation:

The x intercept is,

  $\begin{array}{l}t=-\frac{85}{2\left(-16\right)}\\ =-2.65\end{array}$

Substitute the values in above equation.

  $\begin{array}{c}h=85\left(2.65\right)-16{\left(2.65\right)}^2+6\\ =124.89\end{array}$

Thus, the maximum height gained by arrow is $124.89\text{ft}$ .