Achild and sled with a combined mass of 54.6 kg slide down a frictionless hill that is 8.97m high. if the sled starts from rest what is its speed at the bottom of the him?

Total energy (kinetic plus potential) must be conserved between the top and bottom of the hill. Because the sled starts from rest, and potential energy is zero at the bottom of the hill, PE_initial=KE_final  
m*g*h=0.5*m*v^2  
where m is mass, 54.6 kg 
g is gravitational acceleration, 9.81 m/s^2 
h is height, 8.97 m 
and v is final velocity  
rearranging: v=sqrt(g*h*2)=13.3 m/s