Question

A truck of mass 30,000 kg moves up an inclined plane of slope 1 in 100 at a speed of 30 kmph. The power of the truck is (given$g=10m{{s}^{-1}}$).

Answer 1

Hint: We are given that a truck off mass 30000kg moves up on inclined plane therefore the truck is moving on an incline plane therefore only component of weight $\left( mg\sin \theta \right)$ will oppose the upward motion. So the power dissipated can be calculated.

Formula used:
$\begin{align}
  & \text{power=force}\times{\text{ velocity}} \\
 & P=\left( mg\sin \theta \right)\times v \\
\end{align}$

Complete step by step answer:
As the truck is moving on an incline plane therefore only the component of weight $\left( mg\sin \theta \right)$ will oppose the upward motion.
 Here slope is given 1 and ratio is with 100 so from here we can say that if we draw a right angle triangle then 1 represents the perpendicular side and 100 represents the hypotenuse.
We know that sin $\theta$= $\dfrac{\text{Perpendicular}}{\text{Hypotenuse}}$
sin $\theta$= $\dfrac{\text{1}}{\text{100}}$
$\begin{align}
  & power=force\times velocity \\
 & P=\left( mg\sin \theta \right)\times v \\
 & P=30000\times 10\times \dfrac{1}{100}\times \dfrac{30\times 5}{18}=25kW \\
\end{align}$

Additional Information: Energy is what makes change happen and may be transferred from one object to a different. Energy also can be transformed from one form to another.
Power is the rate at which energy is transferred. It is not energy but is usually confused with energy. The watt is that the most ordinarily used unit of measure for power. It measures the rate of energy transfer.
A watt equals a joule per second. If a sensible phone uses five joules of energy every second, then the facility of the phone is five joules per second, or five watts.

Note: Power can be defined as the rate of doing work. If a work W is performed by a person in time t.
The average power dissipated is $\dfrac{W}{t}$.
Power is a scalar quantity because we know that the power is the ratio of two scalar quantities.
Power of a person is 1 watt if it does work at the rate of 1 joule for 1 second.
The power can also be constant for a given time interval.
Instantaneous power is described as the limiting value of the average power when the time interval approaches to zero.