Climber's Compass Drop Time Calculation

A climber dropped her compass at the end of her 240-meter climb. How long did it take to strike bottom? Group of answer choices

7.0 seconds

77 seconds

70 seconds

8.0 seconds

To determine how long it took for the compass to strike the bottom after being dropped from a height of 240 meters, we can use the formula for the time of free fall under the influence of gravity:

[ d = \frac{1}{2} g t^2 ]

where:

• (d) is the distance fallen (240 meters),
• (g) is the acceleration due to gravity (approximately (9.81 , \text{m/s}^2)),
• (t) is the time in seconds.

Rearranging the formula to solve for (t):

[ t^2 = \frac{2d}{g} ]

Substituting the values:

[ t^2 = \frac{2 \times 240 , \text{m}}{9.81 , \text{m/s}^2} ]

Calculating the right side:

[ t^2 = \frac{480}{9.81} \approx 48.94 ]

Now, taking the square root to find (t):

[ t \approx \sqrt{48.94} \approx 7.0 , \text{seconds} ]

Thus, the time it took for the compass to strike the bottom is approximately 7.0 seconds.

The correct answer is 7.0 seconds.