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Difficulty: MediumGravity and Free Fall

A construction worker on a tall scaffolding accidentally drops a heavy steel wrench. Assuming there is no air resistance and the acceleration due to gravity is 32 ft/s232\text{ ft/s}^2, the wrench hits the ground after exactly 44 seconds. What is the height from which the wrench was dropped, in feet?

Answer: 256 ft

Answer

The wrench was dropped from a height of 256 feet.
The height of the drop is found by calculating the total distance the wrench falls in 4 seconds under the continuous influence of gravity. Using the standard kinematic equation for an object dropped from rest, d=12gt2d = \frac{1}{2}gt^2, and the given gravitational acceleration of 32 ft/s232\text{ ft/s}^2, the calculation is 0.5×32×(42)=16×16=2560.5 \times 32 \times (4^2) = 16 \times 16 = 256 feet.

Step-by-Step Solution

1
Identify the known variables from the problem statement.
Initial velocity vi=0v_i = 0, time t=4 st = 4\text{ s}, gravity g=32 ft/s2g = 32\text{ ft/s}^2.
Establishing the knowns is required to select the appropriate kinematic formula for free fall.
2
Select the correct formula for calculating the distance fallen.
d=12gt2d = \frac{1}{2}gt^2
This formula calculates distance when an object accelerates uniformly from rest.
3
Substitute the known values into the equation and perform the calculation.
d=0.5×32×16=256d = 0.5 \times 32 \times 16 = 256
To compute the final numerical distance.

Key Concept

Calculating distance in free fall using gravitational acceleration
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Topics

Gravity and Free Fall

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