Height of the Cliff: 44.1 Meters

An object is thrown off a cliff with a horizontal speed of 10 m/sec. After 3 seconds the object hits the ground. What is the height of the cliff? Group of answer choices

4.4 meters

41. meters

4.1 meters

44.1 meters

To find the height of the cliff, we can use the formula for the distance fallen under the influence of gravity. The vertical motion of the object is independent of its horizontal motion.

The formula for the distance fallen due to gravity is:

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

where:

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

Given that ( t = 3 ) seconds, we can substitute the values into the formula:

[ d = \frac{1}{2} \times 9.81 , \text{m/s}^2 \times (3 , \text{s})^2 ]

Calculating this step-by-step:

1. Calculate ( (3 , \text{s})^2 = 9 , \text{s}^2 ).
2. Multiply by ( g ): ( 9.81 , \text{m/s}^2 \times 9 , \text{s}^2 = 88.29 , \text{m} ).
3. Now multiply by ( \frac{1}{2} ):

[ d = \frac{1}{2} \times 88.29 , \text{m} = 44.145 , \text{m} ]

Rounding this to one decimal place gives us approximately ( 44.1 , \text{m} ).

Thus, the height of the cliff is **44.1 meters