The boat's engine must provide energy at the rate of \(\boxed{9000\text{ J/s}}\) or \(\boxed{9000\text{ W}}\) or \(\boxed{9\text{ kW}}\).
Explanation:
Given:
The horizontal force required to move the boat is \(6.0\times10^2\text{ N}\).
The speed of the boat under the action of the force is \(1.5\times10^1\text{ m/s}\).
Concept:
The rate at which the energy is required by the boat is nothing but the power at which the motor should operate. The power of a device or a motor is defined as the rate of work done by the motor.
The rate at which the boat's engine must provide energy to move the boat is given by:
\(\boxed{P=F.v}\)
Here, \(P\) is the power of the engine, \(F\) is the force exerted on the boat and \(v\) is the speed of the boat.
Substitute the values in above expression.
\(\begin{aligned}P&=(6.0\times10^2)(1.5\times10^1)\text{ J/s}\\&=9000\text{ J/s}\end{aligned}\)
Thus, The boat's engine must provide energy at the rate of \(\boxed{9000\text{ J/s}}\) or \(\boxed{9000\text{ W}}\) or \(\boxed{9\text{ kW}}\).
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Answer Details:
Grade: Senior School
Subject: Physics
Chapter: Energy and Power
Keywords:
boat, weighing, engine, force, horizontal, direction, velocity, rate, energy, power, provide energy, meters per second.
