Answer: 1.22 m
Explanation:
The equation of motion in this situation is:
(1)
Where:
is the final height of the ball
is the initial height of the ball
is the vertical component of the initial velocity (assuming the ball was thrown vertically and there is no horizontal velocity)
is the time at which the ball lands
is the acceleration due gravity
So, with these conditions the equation is rewritten as:
(2)
(3)
Finally:
Answer:
a) The 2 forces are equal
b) The impulse is the same
c) The change in momentum is the same
d) Inelastic
Explanation:
a)
According to Newton's third law of motion:
"When an object A exerts a force on an object B (action force), then object B exerts an equal and opposite force on object A (reaction force)"
In this problem, we can identify:
- The car as object A
- The bug as object B
Therefore:
- The force exerted by the car on the bug is the action force
- The force exerted by the bug on the car is the reaction force
According to Newton's third law of motion, these two forces are equal in magnitude, and opposite in direction.
b)
The impulse exerted on an object is equal to the product between the force exerted on it and the time taken:
where
I is the impulse
F is the force exerted
is the time during which the force is applied
In this problem:
- The force F exerted on both the car and the bug is the same (according to what we said in part a)
- The time interval is the same for the two objects
Therefore, the impulse exerted on the bug is the same as the impulse on the car.
c)
The change in momentum of an object is defined as:
(1)
where
m is the mass of the object
is the change in velocity of the object
However, according to the impulse theorem, the change in momentum of an object is also equal to the impulse it has experienced:
Therefore, since the impulse experienced by the bug and the car is the same (part b), this means that the change in momentum of the bug and the car is the same (and so by looking at eq.(1), we can conclude that the bug will experience a larger change in velocity, since its mass is smaller than that of the car).
d)
There are two types of collision:
In particular, inelastic collision occurs when the two objects stick together after the collision.
In this situation, we see that the bug and the car stick together after the collision: this means that the total kinetic energy of the system is not conserved, and therefore, this is an example of inelastic collision.
Answer:
1. The car which is twice as massive as the other will have twice potential energy.
Explanation:
The potential energy of an object is given by:
where
m is the mass of the object
g is the gravitational acceleration
h is the height of the object measured to some reference level
In this problem, we have two cars at same elevation (= same h in the formula) but one car has twice the mass of the second car. Calling m the mass of one car and 2m the mass of the second car, we have:
- Potential energy of the first car:
- potential energy of the second car:
So, the car which is twice as massive as the other will have twice potential energy.