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Question: A streamer boat of \(10\,H.P.\) can move with maximum speed \(7.46\,m{s^{ - 1}}\). What is the resis...

A streamer boat of 10 H.P.10\,H.P. can move with maximum speed 7.46 ms−17.46\,m{s^{ - 1}}. What is the resistance (force) offered by the river on the boat?

Explanation

Solution

In the given question a boat has power of 10 H.P.10\,H.P.(horsepower) is moving with a speed of 7.46 ms−17.46\,m{s^{ - 1}}. We have to calculate the resistive force offered by the river on the boat. Resistive force is the force whose direction is opposite to the motion of a body.

Complete step by step answer:
In the given question a boat has power of 10 H.P.10\,H.P.. Power is defined as the rate at which energy is transformed from the electrical energy into some other form. The standard unit of power is Watt(W)Watt(W). The horsepower is a unit in the foot-pound second or English system sometimes used to express the rate at which mechanical energy is converted. So, we have to convert the unit of power in standard time i.e., watts. A power level of 1 H.P.1\,H.P.is approximately equivalent to 746 watts746\,watts (W)(W). So, the given power P=7460 WP = 7460\,W.

And it is given that the boat is moving with a velocity of 7.46 ms−17.46\,m{s^{ - 1}}. The velocity of an object is the rate of change of its position with respect to a frame of reference, and is a function of time. We have to calculate the resistive force i.e., opposing force.
We know that power=Force × velocity\text{power} = \text{Force}\, \times \,\text{velocity}
So, Force=powervelocity\text{Force} = \dfrac{\text{power}}{\text{velocity}}
Putting the given data in the above formula. We get,
⇒Force=74607.46\Rightarrow \text{Force} = \dfrac{{7460}}{{7.46}}
∴Force=1000 N\therefore \text{Force} = 1000\,N

Hence the resistive force offered by the river on the boat is 1000 N1000\,N.

Note: The unit of power is to be converted before solving the problem as we have the unit of velocity in standard units. Power and velocity are the vector quantities that means they have both magnitude and direction. Force is also a vector quantity. A force is defined as push or pull that changes or tends to change the state of rest or uniform motion of a moving object. Standard unit of force is Newton\text{Newton}. Resistive force always opposes the motion of the object.