How long does it take a person to fall 64 feet?
A. 1/3 second
B. 2 seconds
C. 10 seconds
D. 60 seconds
Answer (2)
Use the formula for distance fallen under constant acceleration: d = 2 1 g t 2 .
Plug in the given values: 64 = 2 1 ( 32 ) t 2 .
Solve for t : t 2 = 4 .
Take the square root of both sides: t = 4 = 2 . The time it takes to fall 64 feet is 2 seconds .
Explanation
Understanding the Problem We are given that a person falls 64 feet and we want to find the time it takes to fall this distance. We will assume that the person is falling under the influence of gravity alone, with no air resistance. We will also assume a standard acceleration due to gravity, which is approximately g = 32 ft/s 2 .
Using the Formula for Distance The formula for the distance d an object falls under constant acceleration g in time t is given by: d = 2 1 g t 2
Plugging in the Values We are given d = 64 feet and g = 32 ft/s 2 . We want to solve for t . Plugging in the given values, we have: 64 = 2 1 ( 32 ) t 2
Simplifying the Equation Simplifying the equation, we get: 64 = 16 t 2
Isolating t 2 Dividing both sides by 16, we have: t 2 = 16 64 = 4
Solving for t Taking the square root of both sides, we get: t = 4 = 2 Since time must be non-negative, we take the positive square root.
Final Answer Therefore, it takes 2 seconds for a person to fall 64 feet.
Examples
Imagine you're at the top of a cliff and drop a rock. Knowing how long it takes for the rock to fall a certain distance can help you estimate the height of the cliff. This principle is also used in amusement park rides, like drop towers, where the controlled freefall creates a thrilling experience. Understanding the relationship between gravity, time, and distance is crucial in physics and engineering for designing safe and exciting experiences.
Using the formula for distance fallen under gravity, it takes 2 seconds for a person to fall 64 feet. Therefore, the correct answer is B. 2 seconds.
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