A penny is dropped from the top of a tower. It hits the ground below after 2.5 s. How tall was the tower?
1 answer:
Answer:
C. 30.6m
Explanation:
To find the height of the tower, we are to use Newtons law of motion to solve this problem. Since the penny is falling from the top of the tower, it is acted by the acceleration due to gravity. The formula to be used is:
Where H is the height of the tower, t is the time taken to hit the ground, u is the initial velocity and g is the acceleration due to gravity.
Given that, t = 2.5 s, g =9.8 m/s², u = 0 m/s (at the top of tower)
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a) The acceleration of gravity is
b) The critical velocity is 6668 m/s (24,006 km/h)
c) The period of the orbit is 8452 s
d) The satellite completes 10.2 orbits per day
e) The escape velocity of the satellite is 9430 m/s
f) The escape velocity of the rocket is 11,191 m/s
Explanation:
a)
The acceleration of gravity for an object near a planet is given by
where
G is the gravitational constant
M is the mass of the planet
R is the radius of the planet
h is the height above the surface
In this problem,
(mass of the Earth)
(Earth's radius)
(altitude of the satellite)
Substituting,
b)
The critical velocity for a satellite orbiting around a planet is given by
where we have again:
(mass of the Earth)
(Earth's radius)
(altitude of the satellite)
Substituting,
Converting into km/h,
c)
The period of the orbit is given by the circumference of the orbit divided by the velocity:
where
v = 6668 m/s
Substituting,
d)
One day consists of:
While the period of the orbit is
T = 8452 s
So, the number of orbits completed by the satellite in one day is
e)
The escape velocity for an object in the gravitational field of a planet is given by
where here we have:
Substituting, we find
f)
We can apply again the formula to find the escape velocity for the rocket:
Where this time we have:
, because the rocket is located at the Earth's surface, so its altitude is zero.
And substituting,
Learn more about gravitational force:
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