A $2\mathrm{.}60$ kg box with an initial speed of $4\mathrm{.}50$ m$/$s at the bottom of a $30\mathrm{.}0$o incline is pushed

up the incline by a $15\mathrm{.}0$ N horizontal force. The coefficient of friction between the box and the

incline is $0\mathrm{.}250.$

$30$ o

$2\mathrm{.}6$ kg$15$ N

$($a$)$ What is the magnitude of the frictional force that opposes the motion?

$($b$)$ What is the maximum distance the box travels up the incline? Use energy considerations.

$($c$)$ Use Newton$$s second law to calculate the acceleration of the box up the incline.

$($d$)$ Use your answer from $($c$)$ and calculate the maximum distance the box travels up the

incline using kinematic equations