13. A ball is thrown downward from the top of a building with an initial speed of 25 m/s. It
strikes the ground after 2.0s. How high is the building,. assuming negligible air resistance?
To solve this problem, we can use the equations of motion. The formula that relates the distance traveled by an object in free fall to its initial velocity, time, and acceleration is:
d = V₀t + (1/2)gt²
Where:
- d is the distance traveled
- V₀ is the initial velocity
- t is the time
- g is the acceleration due to gravity (approximately 9.8 m/s²)
In this case, the ball is thrown downwards, so the initial velocity is negative (-25 m/s). The time it takes for the ball to strike the ground is 2.0 s. We want to find the height of the building, which is the distance traveled by the ball before hitting the ground.
Using the equation above, we can calculate the height of the building:
d = (-25 m/s)(2.0 s) + (1/2)(9.8 m/s²)(2.0 s)²
d = -50 m - 19.6 m
d = -69.6 m
Since the height cannot be negative, we take the absolute value of the result:
Height of the building = |d| = 69.6 m
Therefore, the height of the building is 69.6 meters.