Question

A 57-gram tennis ball moving at 70 miles per hour is hit with a 110-gram tennis racquet moving at 60 miles per hour. Which statement best compares the total amounts of mass and energy before and after impact? A. Because the velocities of the ball and racquet are unequal, there is more mass and energy after impact than there is before impact. B. Because the velocities of the ball and racquet are unequal, there is less mass and energy after impact than there is before impact. C. Because neither mass nor energy are conserved, the total amounts of mass and energy are different before and after impact. D. Because mass and energy are both conserved, the total amounts of mass and energy are the same before and after impact.

Answer 1

D. Because mass and energy are both conserved, the total amounts of mass and energy are the same before and after impact.

Step-by-step explanation:

As we know that, the energy in motion is Kinetic Energy mathematically given as:

`KE=(1)/(2) m.v^2`

Now, according to the law of conservation of energy:

`(1)/(2) m_1.u_1^2+(1)/(2) m_2.u_2^2=(1)/(2) m_1.v_1^2+(1)/(2) m_2.v_2^2`

where:

`m_1\ \&\ m_2` mass of racquet and ball respectively and
`u_1\ \&\ u_2` are their respective initial velocities.

`v_1\ \&\ v_2` are the respective final velocities.

Also the law of conservation of momentum is applicable in this case:

`m_1.u_1+ m_2.u_2= m_1.v_1+m_2.v_2`

In this case the velocity of the lighter mass will get increases in the final condition.