Answer
F = 41 N
Work Step by Step
$v = (60 ~km/h)(\frac{1000 ~m}{1 ~km})(\frac{1 ~h}{3600 ~s}) = 17 ~m/s$
We can use kinematics to find the acceleration.
$a = \frac{v^2-v_0^2}{2x} = \frac{(17 ~m/s)^2 - 0}{(2)(75 ~m)} = 1.9 ~m/s^2$
We can use a force equation to find the required force F.
$\sum F = ma$
$F + mg ~sin(\theta) - mg ~cos(\theta)\cdot ~\mu_k = ma$
$F = ma - mg ~sin(\theta) + mg ~cos(\theta)\cdot ~\mu_k $
$F = (22 ~kg)(1.9 ~m/s^2) - (22 ~kg)(9.80 ~m/s^2)~sin(6.0^{\circ}) +(22 ~kg)(9.80 ~m/s^2)~cos(6.0^{\circ})\cdot (0.10)$
$F = 41~N$
The force required to push the bobsled is 41 N.
