An object is given an initial velocity. What will happen to the object if no other forces act on it?
1 answer:
You might be interested in
1) The speed of the skier at the bottom of the valley is 29.7 m/s
2) The speed of the skier at the top of the second hill is 9.9 m/s
3) No, the angle of the hills does not affect the result
Explanation:
1)
We can solve this problem by using the law of conservation of energy. In fact, in absence of friction, the total mechanical energy of the skier is conserved:
where
E is the total mechanical energy
U is the gravitational potential energy
K is the kinetic energy
At the top of the hill, K = 0 since the skier is at rest, so all its energy is potential energy:
(1)
where
m is the mass of the skier
is the acceleration of gravity
h = 45.0 m is the height of the hill
As the skier descends the hill, the potential energy is converted into kinetic energy. At the bottom, all the mechanical energy has been converted into kinetic energy:
where
v is the speed of the skier at the bottom of the hill
Since the total energy is conserved,
And so we find
2)
The top of the next hill is located at a height of
h' = 40.0 m
So the total mechanical energy at the top of the second hill is
where v' is the speed at the top of the second hill.
Since the total mechanical energy must be conserved, we can equate this energy to mechanical energy at the beginning (eq. 1), so we have
and we can now solve for v':
3)
As we saw from the previous equations, the angles of the hill does not enter at all the calculations, so it does not affect the value of the speed of the skier.
The reason for this is that the gravitational potential energy of the skier depends only on the height of the hill, h and h', and not from the length of the path along the hill (and so, not on the angle of the hill), and therefore the angle does not enter the calculation.
Learn more about kinetic energy and potential energy:
#LearnwithBrainly