A child tosses a baseball to his siter, who is hanging out the window of an apartment building. The ball's initial velocity is 18 m/s upward. (Ignore any horizontal motion)
1. How long will it take for the ball to reach its maximum height?
2. The sister catches the ball 3.0 seconds after it leaves her brother's hand. How high is the window?
1. (18 m/s)/g = 1.84 seconds
2. After 3.0 s, the ball will have fallen from its maximum height for 1.16 s.
The maximum height is H = Vo^2/(2g) = 16.53 s
After another 1.16s, is will fall 6.59 m from the maximum value.
16.53 - 6.59 = _____ m
To answer these questions, we need to use the kinematic equations of motion, specifically the equation for vertical motion under constant acceleration.
1. How long will it take for the ball to reach its maximum height?
First, we need to determine the time it takes for the ball to reach its maximum height. Given that the ball's initial velocity is 18 m/s upward and there is no vertical acceleration, we can use the equation for vertical displacement:
d = v₀t + (1/2)at²
Since there is no acceleration in the vertical direction, the equation simplifies to:
d = v₀t
Where:
d = displacement (change in position)
v₀ = initial velocity
t = time
In this case, the displacement is zero at the maximum height, and the initial velocity is 18 m/s upward. Plugging in these values, we can solve for time:
0 = (18 m/s)t
Since anything multiplied by 0 is 0, we can conclude that the time taken to reach the maximum height is 0 seconds. This means that the ball reaches its maximum height instantly and starts to fall back down.
2. How high is the window?
To determine the height of the window, we need to calculate the vertical displacement of the ball when the sister catches it. We can use the same equation used in the first question:
d = v₀t + (1/2)at²
Since the initial velocity is 18 m/s upward and the time is 3.0 seconds, we can plug in these values to solve for the displacement:
d = (18 m/s)(3.0 s) + (1/2)(9.8 m/s²)(3.0 s)²
d = 54 m + 44.1 m
d = 98.1 m
Therefore, the height of the window is 98.1 meters.