Part A The balloon is travelling at 19.8 m/s when it passes Roger's window
Part B The balloon was released from the 7th floor.
To solve the questions, we need to use the equations of motion
<h3>
What are equations of motion?</h3>
Equations of motion are equations used to solve for the motion of an object under a constant acceleration
<h3>Part A How fast are the balloons traveling when they pass Roger's window?</h3>
Since Roger sees water balloons fall past his window and he notices that each balloon strikes the sidewalk 1.01 s after passing his window. Roger's room is on the third floor, 15 m above the sidewalk.
Using the equation of motion s = ut - 1/2gt² where
- s = height of Roger's room above sidewalk = 15 m,
- u = speed of balloon at Roger's window,
- t = time it takes balloon to reach sidewalk = 1.01 s and
- g = acceleration due to gravity = 9.8 m/s²
Making u subject of the formula, we have
u = s/t + 1/2gt
Substiting the values of the variables into th equation, we have
u = s/t + 1/2gt
u = 15 m/1.01 s + 1/2 × 9.8 m/s² × 1.01 s
u = 14.851 m/s + 1/2 × 9.898 m/s
u = 14.851 m/s + 4.949 m/s
u = 19.8 m/s
So, the balloon is travelling at a speed of 19.8 m/s when it passes Roger's window
<h3>Part B From what floor are they being released</h3>
Since the balloons are released from rest, they have zero velocity.
So, using the equation of motion
v² = u² - 2gh where
- u = initial velocity of balloon = 0 m/s (since it is released from rest),
- v = speed of balloon at Roger's window = 19.8 m/s,
- g = acceleration due to gravity = 9.8 m/s² and
- h = height which balloon was released
Making h subject of the formula, we have
h = (v² - u²)/2g
Substituting the values of the variables into ther equation,we have
h = (v² - u²)/2g
h = [(19.8 m/s)² - (0 m/s²)]/2(9.8 m/s²)
h = 392.04 m²/s²/19.6 m/s²)
h = 20 m
Since each floor is 5 m high, so a height of 20 m would be 20 m/5 m = 4 floors.
So, this is 4 floors above Roger's room.
Since roger's room is on the 3rd floor, then 4 floors + 3 floors = 7 floors.
So, the balloon was released from the 7th floor.
Learn more about equations of motion here:
brainly.com/question/27899272
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