Questions: 3.1.6 Quiz: Free Fall Question 1 of 10 A stuntman jumps from the roof of a building to the safety net below. How far has the stuntman fallen after 2.3 seconds? A. 25.9 m B. 9.8 m C. 11.3 m D. 21.2 m SUBMIT PREVIOUS

Solution Steps

In this problem, we are dealing with free fall, which means the only force acting on the stuntman is gravity. The acceleration due to gravity is \( g = 9.8 \, \text{m/s}^2 \). The time of fall is given as \( t = 2.3 \, \text{s} \).

The formula to calculate the distance fallen under constant acceleration (gravity) is: \[ d = \frac{1}{2} g t^2 \] where \( d \) is the distance fallen, \( g \) is the acceleration due to gravity, and \( t \) is the time.

Substitute \( g = 9.8 \, \text{m/s}^2 \) and \( t = 2.3 \, \text{s} \) into the formula: \[ d = \frac{1}{2} \times 9.8 \times (2.3)^2 \]

First, calculate \( (2.3)^2 \): \[ (2.3)^2 = 5.29 \] Now, calculate the distance: \[ d = \frac{1}{2} \times 9.8 \times 5.29 = 25.9461 \, \text{m} \]

Round the result to one decimal place to match the options provided: \[ d \approx 25.9 \, \text{m} \]

Final Answer