Galileo\'s great-great-great grandchild stands at the top of a vertical tower 53
ID: 2275709 • Letter: G
Question
Galileo's great-great-great grandchild stands at the top of a vertical tower 53.4 m tall with a Chianti bottle.
How long does it take for the bottle to fall to the ground, if it was just dropped from the tower?
What is the velocity of the bottle as it hits the ground, if it was just dropped from the tower?
How far does the bottle land from a point on the ground directly beneath the point from which it was launched, if the bottle was thrown straight out horizontally from the tower with a speed of 10.9 m/s?
What is the bottle's horizontal component of velocity, if the bottle was thrown straight out horizontally from the tower with a speed of 10.9 m/s?
What is the magnitude of its velocity just before it strikes the ground, if the bottle was thrown straight out horizontally from the tower with a speed of 10.9 m/s?
Explanation / Answer
How long does it take for the bottle to fall to the ground, if it was just dropped from the tower?
53.4 = 0.5*9.8*t^2
t = 3.3 s
What is the velocity of the bottle as it hits the ground, if it was just dropped from the tower?
v = 0 + 9.8*3.3 = 32.34 m/s
How far does the bottle land from a point on the ground directly beneath the point from which it was launched, if the bottle was thrown straight out horizontally from the tower with a speed of 10.9 m/s?
d = vt = 10.9*3.3 = 35.97 m
What is the bottle's horizontal component of velocity, if the bottle was thrown straight out horizontally from the tower with a speed of 10.9 m/s?
There is no force in horizontal direction. Therefore horizontal component of velocity remains same.
= 10.9 m/s
What is the magnitude of its velocity just before it strikes the ground, if the bottle was thrown straight out horizontally from the tower with a speed of 10.9 m/s?
vx = 10.9 m/s
vy = g * t = 9.8 * 3.3 = 32.34 m/s
v = sqrt(vx^2 + vy^2) = sqrt(10.9^2 + 32.34^2) = 34.13 m/s
Ans: 34.13 m/s
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