1)A student at a window on the second floor of a high school building sees his math teacher coming along a walkway besides the building. He drops a water balloon from 18.0 m above the ground when it the teacher is 1.00 m from the point directly beneath the window. If the teacher is 170 cm tall and walks at a rate of 0.45 m/s, does the balloon hit his head? Does it him at all?
thank you very much
The teacher's head is H = 18.0 - 1.7 = 16.3 m below the window from which the water balloon is dropped. The time required to fall that distance is
t = sqrt(2H/g) = 1.82 s.
The teacher moves horizontally
t*0.45 m/s = 0.82 m in that time. If he was 1.0 m behind the impact point when it was dropped, he will be 0.18 m behind the impact point when the water balloon reaches the height of his head.
That's pretty close. You need to consider the finite size of the water balloon and the person before deciding on an answer. The teacher will have moved even closer to the balloon before it hits the ground.
I would say the water balloon would barely miss his head but probably hit his forward-extended leg before it hits the ground.
To solve this problem, we can use the equations of motion to determine the time it takes for the water balloon to fall and the horizontal distance the teacher moves during that time.
First, let's calculate the time it takes for the water balloon to fall from a height of 16.3 meters above the teacher's head. We can use the equation:
t = sqrt(2H/g)
where H is the height of the balloon above the teacher's head and g is the acceleration due to gravity. Plugging in the values, we get:
t = sqrt(2 * 16.3 / 9.8)
≈ 1.82 seconds
Next, let's calculate the horizontal distance the teacher moves during this time. We can use the equation:
d = vt
where d is the distance, v is the velocity, and t is the time. Plugging in the values, we get:
d = 0.45 * 1.82
≈ 0.82 meters
Since the teacher was initially 1.00 meter from the point directly beneath the window, he would be 0.18 meters behind the impact point when the water balloon reaches the height of his head.
Considering the finite size of the water balloon and the person, it is likely that the water balloon would hit the teacher's forward-extended leg before hitting the ground. The balloon would barely miss his head but come close enough to touch him.