Chapter 9.4, Problem 66PFA

To determine

Find the solution.

Answer to Problem 66PFA

Option D $\frac{\sqrt{15}}{2}$ seconds

Explanation of Solution

Given Information: $h=-16t^2+60$

Formula Used: Quadratic formula

Calculation:

The quadratic equation gives the height of the leaf from its starting position, which is 60 feet above ground.

  $h=-16t^2+60$

To find time it takes to fall 60 feet, means the ground level, where height is equal to 0 Or, $h=0$

  $0=-16t^2+60$

So, simplify

  $16t^2=60$

Now, square root both sides.

  $t=\frac{\sqrt{60}}{\sqrt{16}}$

Now,

  $t=\frac{\sqrt{2\times 2\times 3\times 5}}{\sqrt{2\times 2\times 2\times 2}}$

Now, pair of prime numbers given out

  $t=\frac{2\sqrt{3\times 5}}{2\times 2}$

Hence,

  $t=\frac{\sqrt{15}}{2}$ seconds

So, it takes the leaf about $\frac{\sqrt{15}}{2}$ seconds to fall 60 feet.