The length of the track itself is 500m. The vehicles (each of mass 15kg) are dragged
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Answer:
Assumption: the air resistance on this ball is negligible. Take .
a. The momentum of the ball would be approximately two seconds after it is tossed into the air.
b. The momentum of the ball would be approximately three seconds after it reaches the highest point (assuming that it didn't hit the ground.) This momentum is smaller than zero because it points downwards.
Explanation:
The momentum of an object is equal its mass
times its velocity
. That is:
.
Assume that the air resistance on this ball is negligible. If that's the case, then the ball would accelerate downwards towards the ground at a constant . In other words, its velocity would become approximately
more negative every second.
The initial velocity of the ball is . After two seconds, its velocity would have become
. The momentum of the ball at that time would be around
.
When the ball is at the highest point of its trajectory, the velocity of the ball would be zero. However, the ball would continue to accelerate downwards towards the ground at a constant . That's how the ball's velocity becomes negative.
After three more seconds, the velocity of the ball would be . Accordingly, the ball's momentum at that moment would be
.
1) In a perfectly inelastic collision, the two balls stick together after the collision. In this type of collision, the total kinetic energy of the system is not conserved, while the total momentum is conserved.
If we call
the final velocity of the two balls that stick together, the conservation of the total momentum before and after the collision can be written as
(1)
where
is the mass of ball A
is the mass of ball B
is the initial velocity of ball A
is the initial velocity of ball B (taken with a negative sign, since it goes in the opposite direction of ball A)
If we solve (1) to find, we find that the final velocity of the balls is
and the positive sign means the two balls are going to the right.
2) I assume here we are talking about an elastic collision. In this case, both total momentum and total kinetic energy are conserved:
where
is the final velocity of ball A
is the final velocity of ball B
If we solve simultaneously the two equations, we find:
So, after the collision, ball A moves to the left with velocity v=-2 m/s and ball B moves to the right with velocity v=16 m/s.
3) The total momentum before and after the collision is conserved.
In fact, the total momentum before the collision is:
and the total momentum after the collision is:
If we call
where
If we solve (1) to find
and the positive sign means the two balls are going to the right.
2) I assume here we are talking about an elastic collision. In this case, both total momentum and total kinetic energy are conserved:
where
If we solve simultaneously the two equations, we find:
So, after the collision, ball A moves to the left with velocity v=-2 m/s and ball B moves to the right with velocity v=16 m/s.
3) The total momentum before and after the collision is conserved.
In fact, the total momentum before the collision is:
and the total momentum after the collision is: