A 170 kg physics professor has fallen into the Grand Canyon. Luckily, he managed to grab a branch and is now hanging 53 m below the rim. A student (majoring in linguistics and physics) decides to perform a rescue/experiment using a nearby horse. After lowering a rope to her fallen hero and attaching the other end to the horse, the student measures how long it takes for the horse to pull the fallen physicist to the rim of the Grand Canyon.

The acceleration of gravity is 9.8 m/s2.
If the horse’s output power is truly 1 horsepower (746 W), and no energy is lost to friction, how long should the process take?
Answer in units of s

t= mgh/746

To calculate the time it takes for the horse to pull the physics professor to the rim of the Grand Canyon, we need to find the work done by the horse and then use it to determine the time.

The work done by the horse is given by the equation: Work = Power × time.

Given that the power of the horse is 1 horsepower, which is equal to 746 Watts, we have:

Work = 746 W × time.

Now, we need to find the work done by the horse. The work done is equal to the change in potential energy of the professor.

The potential energy is given by the equation: Potential Energy = mass × gravity × height.

Given that the mass of the professor is 170 kg, the acceleration due to gravity is 9.8 m/s^2, and the height is 53 m, we have:

Potential Energy = 170 kg × 9.8 m/s^2 × 53 m.

Substituting this into the work equation, we have:

746 W × time = 170 kg × 9.8 m/s^2 × 53 m.

Simplifying, we find:

746 W × time = 85,949.6 kg·m^2/s^2.

To isolate time, we divide both sides of the equation by 746 W:

time = 85,949.6 kg·m^2/s^2 ÷ 746 W.

Calculating this, we find:

time = 115.4 s.

Therefore, it should take approximately 115.4 seconds for the horse to pull the physics professor to the rim of the Grand Canyon.

To determine how long it will take for the horse to pull the physics professor to the rim of the Grand Canyon, we can use the concept of power.

Power is defined as the rate at which work is done, and it is given by the equation:

Power = Work / Time

In this case, the power of the horse is given as 1 horsepower, which is equal to 746 watts. We can use this information to find the work done by the horse.

The work done by the horse is equal to the force applied by the horse multiplied by the distance over which the force is applied. In this case, the force applied by the horse is equal to the weight of the professor, which can be calculated using the equation:

Weight = mass * acceleration due to gravity

Weight = 170 kg * 9.8 m/s^2

Next, we need to calculate the distance over which the force is applied. The distance is given as 53 m.

With the force and distance known, we can calculate the work done by the horse using the equation:

Work = Force * Distance

Now that we have the work done by the horse, we can rearrange the power equation to solve for time:

Time = Work / Power

Plugging in the values we have calculated, we can now solve for time:

Time = (Force * Distance) / Power

Time = (Weight * Distance) / Power

Time = (170 kg * 9.8 m/s^2 * 53 m) / 746 W

Calculating this equation will give us the time it takes for the horse to pull the professor to the rim of the Grand Canyon.