Final answer:
The speed of the ball when it hit the ground was 18.62 m/s. The average speed during the 1.9 seconds was 1.05 m/s. The height of the window was 1.8 meters.
Step-by-step explanation:
In order to solve this problem, we can use the equations of motion for objects in free fall. Let's break down the problem into three parts:
- (a) What was the ball's speed when it hit the ground?
- Since the ball was dropped from rest, we can use the equation:
- vf = vi + gt
- Where
- vf
- is the final velocity,
- vi
- is the initial velocity (which is 0 since the ball was dropped from rest),
- g
- is the acceleration due to gravity (9.8 m/s²), and
- t
- is the time (1.9 seconds). Plugging in the values, we get:
- vf = 0 + (9.8)(1.9) = 18.62 m/s
- So the ball's speed when it hit the ground was 18.62 m/s.
- (b) What was the ball's average speed during the 1.9 seconds?
- The average speed is defined as the total distance traveled divided by the total time. Since the ball was dropped and fell straight down, the distance is equal to the height of the window. Using the equation:
- avg speed = distance / time
- We can calculate the average speed as:
- avg speed = (2.00 m) / (1.9 s) = 1.05 m/s
- So the ball's average speed during the 1.9 seconds was 1.05 m/s.
- (c) How high was the window?
- Since the ball was dropped from rest, we can use the equation:
- h = vi * t + (1/2) * g * t²
- Where
- h
- is the height of the window,
- vi
- is the initial velocity (0 m/s),
- t
- is the time (1.9 seconds), and
- g
- is the acceleration due to gravity (9.8 m/s²). Plugging in the values, we get:
- h = 0 + (1/2)(9.8)(1.9)² = 1.8 m
- So the height of the window is 1.8 meters.