Finding the speed of an object

Question

A certain horse can maintain 1.0 hp of output for 2.4 hours with an efficiency of 72%. The horse is pulling a 220 kg object along a horizontal ground. The coefficient of kinetic friction between the ground and the object is 0.46. Find the speed of the object.

 

The answer is supposed to be 0.54 m/s but I have no idea how to arrive at the answer

 

I know that the work done by friction is 992d, and the power input is 1036 W

 

Answer 1

You need to multiply the stated power by the efficiency to get the actual power, and then set that equal to the product of force and speed.  Set the force equal to the force of friction, and then you can solve for speed.

 

P = stated power = 1.0 hp = 745.7 watts

 

η = efficiency = 0.72

 

ηP = actual power

 

ηP = Fv = (μmg)v ⇒

 

v = ηP / (μmg) = 0.72(745.7) / [0.46(220)(9.8)] m/s ≅ 0.541 m/s