Question

The time $t$ in seconds that it takes an object to fall a distance from $d$ ft from rest is given the formula $\sqrt[]{2d/8}$ where g is the acceleration due to gravity. Find the value of d when g = 32 ft/s² and $t$ = 3 s.

Answer 1

Answer:

144 ft

Explanation:

t = √(2d/g)

3 s = √(2d / (32 ft/s²))

9 s² = 2d / (32 ft/s²)

d = 144 ft

Answer 2

Answer:

d = 144 ft

General Formulas and Concepts:

Math

• Order of Operations: BPEMDAS

Physics

• Vertical Kinematics Equation: d  = 1/2gt²

• Gravity g is always equal to 9.8 m/s² or 32 ft/s²

Explanation:

Step 1: Define

$t=\sqrt{\frac{2d}{g} }$ - we get this from algebraically solving to t from the kinematics equation

g = 32 ft/s²

t = 3 seconds

Step 2: Solve

1. Substitute:                                   $3=\sqrt{\frac{2d}{32} }$
2. Square both sides:                      $9=\frac{2d}{32}$
3. Multiply 32 on both sides:          $288=2d$
4. Divide 2 on both sides:               $144=d$
5. Rewrite:                                        $d=144$