Chapter 9.4, Problem 59HP

To determine

Find the solution.

Answer to Problem 59HP

2 seconds

Explanation of Solution

Given Information: Velocity $v=29ft/\sec$ and Height $h=6$ ft.

Formula Used: Factorization

Calculation:

Velocity $v=29ft/\sec$ and Height $h=6$ ft.

So,

  $16t^2-29t-6=0$

The shot put hits the ground when $h(t)=0$

So,

  $16t^2-32t+3t-6=0$

So,

  $16t^2-32t+3t-6=0$

So,

  $16t\left(t-2\right)+3\left(t-2\right)=0$

Now,

  $\left(16t+3\right)\left(t-2\right)=0$

Now,

  $\left(16t+3\right)=0$ or $t-2=0$

Hence,

  $t=\frac{-3}{16}$ or $t-2=0$

Taking the positive value for t, get that it takes 2 seconds to hit the ground.