Question

A car has wheels of diameter $70m$ . How many revolutions can the wheel complete in $20$ minutes if the car is travelling at a speed of $110m/s$?

Answer 1

Hint: Here in this question from the given information we can calculate the distance travelled by the car in $20$ minutes from the formula,
Distance travelled by the car $ = $speed of the car $ \times $ time taken
As that distance is covered by the revolutions of the wheels of the can, so we can say that
No. of revolutions will be equal to the total distance travelled divided by the perimeter of the wheels or distance covered by one revolution of the wheels.
That is, No. of revolutions$ = $ total distance covered$ \div $(distance covered by one revolution of the wheels)

Complete step-by-step answer: Here in this question we will start solving after enlisting the given information.
So, it is given in this question that,
A car has wheels of diameter $70m$
The car is travelling at a speed of $110m/s$
And we need to find how many revolutions can the wheel complete in $20$ minutes.
So, from the given information firstly we will find the total distance covered by the car in $20$ minutes.
So, now as we know that Distance travelled by the car $ = $speed of the car $ \times $ time taken
Here the speed of the car and the time taken is given in the question,
That is, speed of the car $ = 110m/s$ and time taken$ = 20$ minutes.
So, by putting the corresponding values we get,
Distance travelled by the car $ = 110 \times \left( {20 \times 60} \right)m$ (as $1$minute$ = 60$seconds)
So, Distance travelled by the car $ = 132000m$
Now, we need to find how much distance is covered by one revolution of the wheel, so that by dividing the distance travelled from it we will get our the no. of revolutions taken place.
So, Distance travelled by one revolution$ = \pi d$ (where $d$ is the diameter of wheel)
As it is given in the question that $d = 70m$
So, by putting the corresponding values we get,
Distance travelled by one revolution$ = \pi \left( {70} \right)m$
Distance travelled by one revolution$ = 220m$ (As $\pi = \dfrac{{22}}{7}$)
So, we can say that No. of revolutions is equal to the total distance travelled divided by the distance travelled by one revolution.
So, No. of revolutions$ = $ (the total distance travelled)$ \div $(the distance travelled by one revolution)
Here as we derived above that
The total distance travelled$ = 132000m$, Distance travelled by one revolution$ = 220m$
So, by putting corresponding values we get
 No. of revolutions$ = \dfrac{{132000}}{{220}}$
No. of revolutions$ = 600$

Note: Here in this question we needed to know that the distance is travelled when the wheel makes revolutions, which means the distance travelled will always have a factor which is the distance travelled in one revolution, that is the distance travelled by the vehicle is equal to the multiplication of no. of revolutions of the wheel with the distance travelled by one revolution.