Question

Two cars moving in the same direction with a speed of 30km/h. they are separated from each other by 5km. a third car moving in the opposite direction meets the two cars after an interval of 4min. What is the speed of the third car?
$\begin{aligned} & \text{A}\text{. 30km}{{\text{h}}^{-1}} \\\ & \text{B}\text{. 35km}{{\text{h}}^{-1}} \\\ & \text{C}\text{. 40km}{{\text{h}}^{-1}} \\\ & \text{D}\text{. 45km}{{\text{h}}^{-1}} \\\ \end{aligned}$

Answer 1

Hint: This is a question of relativity. This kind of question can be solved by using the concept of relativity and relative speed. Since in this question, the speed and direction of both the cars is the same therefore relative speed will be zero. Calculate speed of third with respect to those two cars. Use the formula of velocity. Since the speed given in the question is in km/h, so convert 4min into hour.

Complete step by step solution:
In this question, it is given that two cars are moving in the same direction and these two car are separated by a distance 5km. The speed of both cars is the same which is 30km/hr. Now a third car is moving opposite to that two cars. We need to find out the speed of the third car if it meets the two cars at an interval of 4 minutes.
As we can see in the question, the speed of both the cars is the same and they are moving in the same direction therefore their relative speed between two cars is zero.
Now let’s find the relative velocity of the third car with respect to two cars.
So, relative velocity of third car=$\dfrac{5km}{\dfrac{4}{60}h}=75km/h$
Now we need to find the actual velocity of the third car. Actual velocity of a car can be calculated by subtracting 30km/h from calculated 75km/hr.
Therefore, the actual velocity of the third car is 75-30 =45km/h.
Therefore the speed of the third car is 45km/h i.e. $45km{{h}^{-1}}$.
Answer- (D)

Note: In this question, we need to use the concept of relativity. Note that both the cars have the same speed and direction. So the relative speed must be zero. Look for options, options are in km/h in units. So convert the answer according to the unit. Things in relativity are different than in mechanics. Some students may get confused in the speed and velocity formula. Speed is nothing but distance per unit time while velocity is nothing but displacement per unit time.