Answer to Question #150381 in Classical Mechanics for Jacob stan

Question

A child starts sledding from rest, going down a 40-m-long 7.5° incline, then coasting across a horizontal stretch. The mass of sled + child is 35 kg, and the coefficient of kinetic friction is 0.060.
What is the total time for the ride?

Answer 1

$\text {inclined track:}$

$F_1=ma_1$

$a_1=g(\sin \theta -\mu \cos \theta )$

$a_1 = 9.8(sin7.5^0-0.06*cos 7.5^0) = 0.7$

$s = V_0t_1+\frac{a_1t_1^2}{2};V_0=0$

$t_1 = \sqrt{\frac{2s}{a_1}}=\sqrt{\frac{2*40}{0.7}}=10.7$

$V_1 = V_0+at_1$

$V_1=0.7*10.7 =7.49$

$\text{horizontal track:}$

$F_2=ma_2$

$a_2= \mu*g$

$V_2= V_0-at_2$

$V_2=0 \text{ stop motion}$

$V_0 = 7.49 \text{ speed at the end inclined track}$

$t_2= \frac{V_0}{a_2}=\frac{V_0}{\mu*g}=\frac{7.49}{9.8*0.06}=12.7$

$\text{All time:}$

$t = t_1+t_2 = 12.7+10.7 = 23.4$

Answer:total time 23.4 seconds