A small rock bounces off the windshield of a moving car and experiences a large change in velocity. How does the car’s momentum change?(1 point)
Responses
It has a much smaller change in momentum than that of the rock, in the opposite direction.
It has a much smaller change in momentum than that of the rock, in the opposite direction.
It has a change in momentum equal to that of the rock, in the opposite direction.
It has a change in momentum equal to that of the rock, in the opposite direction.
It does not change.
It does not change.
It has a change in momentum greater than that of the rock, in the opposite direction.
It has a change in momentum greater than that of the rock, in the opposite direction.
It has a change in momentum equal to that of the rock, in the opposite direction.
The correct response is:
It has a change in momentum equal to that of the rock, in the opposite direction.
To determine how the car's momentum changes when a small rock bounces off its windshield, we need to consider the principles of conservation of momentum.
The momentum of an object is given by the product of its mass and velocity. Mathematically, momentum (p) can be calculated as p = m * v, where m is the mass and v is the velocity.
Initially, before the rock collides with the windshield, the momentum of the car is given by the product of its mass and velocity (m_car * v_car). At this point, the rock has zero initial momentum (m_rock * v_rock = 0), as it is stationary.
When the rock bounces off the windshield and rebounds in the opposite direction, it gains momentum in the direction of its new velocity. This change in momentum is equal to the product of the rock's mass (m_rock) and its final velocity (v_rock). Therefore, the rock experiences a change in momentum of Δp_rock = m_rock * v_rock.
According to Newton's third law of motion, for every action, there is an equal and opposite reaction. So, when the rock imparts momentum onto the car's windshield, an equal and opposite change in momentum is experienced by the car itself. Therefore, the car's momentum changes by an amount equal to the product of its mass (m_car) and the final velocity of the rock (v_rock), in the opposite direction. This change in momentum of the car can be represented as Δp_car = m_car * (-v_rock), which simplifies to Δp_car = -m_car * v_rock.
Comparing the magnitudes of the changes in momentum, we can conclude that the change in momentum of the car is greater than that of the rock. Additionally, since the car's momentum change is in the opposite direction as the rock's final velocity, the correct statement is: "It has a change in momentum greater than that of the rock, in the opposite direction."