In mid-nineteenth century England horses were often used to pull barges along canals. The horse, naturally, trudged along a path parallel to the canal and so the rope to the barge was at an angle to the motion of the barge.

a) If such a horse was pulling with a force of 155 N at a speed of 12.60 km/h and the angle of the rope with respect to the canal direction was 35.0 degrees how much work (in KJ) does the horse do in 9.1 minutes ?
b) What is the average power ? (Give your answer in HP, Remember: 1HP = 746 W)

work=155*cos35*speed*time

change km/hr to m/s, and time to seconds.

for hp, work/time * 1/746 hp

To calculate the work done by the horse and the average power, we can use the formulas:

a) Work (in joules) = force (in newtons) * distance (in meters)
b) Average power (in watts) = work (in joules) / time (in seconds)

First, let's convert the given values into SI units:
- Speed: 12.60 km/h = 12.60 * 1000 / 3600 = 3.50 m/s
- Angle: 35.0 degrees

Now, let's calculate the distance traveled by the horse in 9.1 minutes:
Time: 9.1 minutes = 9.1 * 60 = 546 seconds
Distance = speed * time = 3.50 * 546 = 1907 meters

a) To calculate the work done by the horse:
Work = force * distance * cos(angle)
Work = 155 * 1907 * cos(35.0)
Work = 155 * 1907 * 0.819
Work ≈ 252,305 joules = 252.305 kJ (rounded to three decimal places)

b) To calculate the average power:
Power = Work / time
Power = 252,305 / 546
Power ≈ 462 watts

To convert watts to horsepower (HP):
Average power (in HP) = Power / 746
Average power ≈ 462 / 746
Average power ≈ 0.62 HP (rounded to two decimal places)

Therefore, the work done by the horse is approximately 252.305 kJ and the average power is approximately 0.62 HP.