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

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

Step-by-step explanation:

Step 1: Define

`t=\sqrt{(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{(2d)/(32) }`
2. Square both sides:
   `9=(2d)/(32)`
3. Multiply 32 on both sides:
   `288=2d`
4. Divide 2 on both sides:
   `144=d`
5. Rewrite:
   `d=144`

Answer 2

144 ft

Step-by-step explanation:

t = √(2d/g)

3 s = √(2d / (32 ft/s²))

9 s² = 2d / (32 ft/s²)

d = 144 ft