Question

Carmine drops a ball at shoulder height from the top of a building (building is 35 feet tall, Carmine is 5 feet tall). If the ball is at rest, and is simply dropped, how long will it take, to the nearest tenth of a second, to hit the ground?

Answer 1

Using the equation of motion for free fall, the time it takes for a ball dropped from 40 feet to hit the ground is calculated to be approximately 1.6 seconds when converted to meters and using the acceleration due to gravity.

Step-by-step explanation:

To calculate the time it will take for a ball dropped from a height to hit the ground, we can use the equations of motion for an object in free fall. The ball is dropped from Carmine's shoulder height, meaning the total height from which it falls is 35 feet from the building plus 5 feet of Carmine's height, totaling 40 feet. Since we typically use the metric system in physics, we first convert 40 feet to meters (1 foot = 0.3048 meters) which gives us approximately 12.192 meters

The formula for the time t it takes an object to fall from rest under gravity is derived from the equation d = 1/2 g t^2, where d is the distance fallen, g is the acceleration due to gravity (9.8 m/s2), and t is the time in seconds. Rearranging the formula to solve for time, we get t = √(2d/g).

Plugging in the values:
t = √(2 * 12.192 / 9.8) ≈ √(2.487) ≈ 1.6 seconds.

So, to the nearest tenth of a second, it will take 1.6 seconds for the ball to hit the ground.