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Question 1182537: Kendra is having her breakfast on a balcony, 20m high when she accidentally knocks down a flower pot. A man, 10m away, is innocently walking along the street at a constant velocity of 4 m/s when the pot fell. Will the innocent man be hit by the pot or will he miraculously be able to avoid the impending accident? The man is 1.7m tall. Explain and prove your answer.
Answer by math_tutor2020(3817)   (Show Source):
You can put this solution on YOUR website!
The man is walking 4 m/s. Let's find out how long it takes him to walk 10 meters.
distance = rate*time
time = distance/rate
time = (10 m)/(4 m/s)
time = (10/4) sec
time = 2.5 sec
It takes 2.5 seconds for him to walk the 10 m distance.
Now let's see how long it takes the pot to fall 20 meters. We'll use this formula
y = 0.5*g*t^2
where,
y = vertical distance the object falls
g = acceleration of gravity
t = elapsed time in seconds
We'll ignore air friction.
In this case,
y = 20
g = 9.81 approximately
So,
y = 0.5*g*t^2
20 = 0.5*9.81*t^2
20 = 4.905*t^2
4.905t^2 = 20
t^2 = (20)/(4.905)
t^2 = 4.07747196738022
t = sqrt(4.07747196738022)
t = 2.0192751093846
t = 2.02
It takes about 2.02 seconds for the pot to fall 20 meters
Since the flower pot's time frame (2.02 seconds) is less than that of the man's overall time frame (2.5 seconds), this means the falling object will hit the ground before the man arrives directly underneath the object. So the object will not hit the man.
This is based on a few assumptions:
1) The pot only hits the man if he traveled exactly 10 meters
2) The pot does not hit his toes
Edit: the man's height is never used. We ignore it because the pot hit the ground before the man arrived at his marker.
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