A ball is held at a height H above a floor. It is then released and falls to the floor. If air resistance can be ignored, which
of the five graphs below correctly gives the mechanical energy E of the Earth-ball system as a function of the altitude y of the ball?
1 answer:
Answer:
Straight line graph attached showing mechanical energy on x-axis and altitude y on y-axis
Explanation:
As mechanical energy is the sum of kinetic energy and potential energy, the ball at a height H possesses potential energy= m.g.H
and Kinetic energy= 0.
But the sum of both energies is equal to m.g.H.
When the ball starts moving, the height starts to decrease and potential energy also decreases with decreasing y. On the other hand kinetic energy starts increasing with decreasing Y. But their sum remains constant i.e equal to mechanical energy. It remains same until the ball touches the ground. The graph attached shows height H or altitude y on x-axis and Mechanical Energy on y-axis. It shows a straight horizental line showing that mechanical energy remains same as y decreases.
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where
is the car's speed
is the duration of the car ride
Similarly, the distance covered by train is equal to the product between the train's speed and the duration of the train ride, 7 h:
The total distance covered is S=255 km, which is the sum of the distances covered by car and train:
which becomes
(1)
we also know that the train speed is 5 km/h greater than the car's speed:
(2)
If we put (2) into (1), we find
and if we solve it, we find
So, the car speed is 20 km/h and the train speed is 25 km/h.
where
Similarly, the distance covered by train is equal to the product between the train's speed and the duration of the train ride, 7 h:
The total distance covered is S=255 km, which is the sum of the distances covered by car and train:
which becomes
we also know that the train speed is 5 km/h greater than the car's speed:
If we put (2) into (1), we find
and if we solve it, we find
So, the car speed is 20 km/h and the train speed is 25 km/h.