$($TM $2-41)$ A train moves along the tracks at a constant speed u$.$ A woman on the train throws

a ball of mass m straight ahead at a speed v with respect to herself.

$($a$)$ What is the kinetic energy gain of the ball as measured by a person on the train?

$($b$)$ What is the kinetic energy gain of the ball as measured by a person standing by the railroad

tracks?

$($c$)$ How much work is done by the woman throwing the ball?

$($d$)$ How much work is done by the train?