Galileo\'s great-great-great grandchild stands at the top of a vertical tower 57
ID: 1871227 • Letter: G
Question
Galileo's great-great-great grandchild stands at the top of a vertical tower 57.8 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? 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 12.9 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 12.9 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 12.9 m/s?
Explanation / Answer
Given:
Height of the tower H = 57.8 m
(a)
from the kinematic relation
s = ut+1/2at2 ....... (1) (s = H = 57.8 m )
a is the acceleration due to gravity (9.8)
t = sqrt (2s/a)
= sqrt(2*57.8m/9.8m/sec2)
= 3.43 sec
(b)
final velocity of the when touches the ground
v = sqrt (2gh)
= sqrt[(2)*(9.8m/sec2)*(57.8m)]
= 33.65 m/sec
(c)
now in this case the bottle is treated as a projectile .
so initial velocity of the projectile u = 12.9 m/sec
Range r = u*t
= (12.9 m/sec)(3.43 sec)
= 44.249m
(d)
Horizontal component of velocity is constant at any point of path of the projectile so
horizontal component of velocity = 12.9 m/sec.
(e)
horizontal velocity u = 12.9 m/sec
vertical velocity v = 33.65 m/sec
resultant velocity at the point where it touches the ground
V = sqrt [(12.9)2+(33.65)2]
= 36.037m/sec.
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