Two cars A and B are going in some directions. A is going was at 60km/h and B is going south at 48km/h. Both of them are approaching towards a junction(intersection) at what rate are they approaching each other when A is 400m and B is 300m from the junction
To find the rate at which the two cars are approaching each other, we can use the concept of relative motion. We need to find the relative velocity between the two cars.
Car A is moving at a velocity of 60 km/h towards the junction. Since we are interested in the relative motion between the two cars, we can consider the velocity of Car A as positive.
Car B is moving towards the junction as well, but in the opposite direction. So, we consider its velocity as negative. Car B is moving south at 48 km/h, which is equivalent to -48 km/h in the context of relative motion.
Let's denote the distance between the cars as d. At the given moment, Car A is 400m away from the junction, and Car B is 300m away from the junction. Therefore, the distance between the two cars is:
d = 400m + 300m
d = 700m
To find the rate at which the cars are approaching each other, we need to find the derivative of d with respect to time (t).
Differentiating both sides of the distance equation with respect to time, we get:
d/dt = dA/dt + dB/dt
where dA/dt is the rate at which Car A approaches the junction and dB/dt is the rate at which Car B approaches the junction.
Since Car A has a constant velocity of 60 km/h, its rate of approach is:
dA/dt = 60 km/h
Car B is moving towards the junction with a velocity of -48 km/h. So, its rate of approach would be:
dB/dt = -48 km/h
Substituting these values back into the relative velocity equation, we get:
d/dt = 60 km/h + (-48 km/h)
d/dt = 12 km/h
Therefore, the two cars are approaching each other at a rate of 12 km/h.
To find the rate at which the two cars are approaching each other, we need to calculate the relative velocity between them.
Let's assume that car A is traveling towards the junction and car B is moving away from the junction.
The velocity of car A towards the junction is given as 60 km/h.
The velocity of car B away from the junction is given as 48 km/h.
To convert the velocities to meters per second (m/s), we will use the conversion factor: 1 km/h = 1000 m/3600 s. Therefore:
Velocity of car A towards the junction = 60 km/h = (60 * 1000 m) / (3600 s) = 60000/3600 m/s ≈ 16.67 m/s
Velocity of car B away from the junction = 48 km/h = (48 * 1000 m) / (3600 s) = 48000/3600 m/s ≈ 13.33 m/s
Now, let's calculate the relative velocity.
Relative velocity = Velocity of car A towards the junction + Velocity of car B away from the junction
= 16.67 m/s + (-13.33 m/s) (as B is going in the opposite direction)
Relative velocity = 16.67 m/s - 13.33 m/s = 3.34 m/s
Therefore, the rate at which the two cars are approaching each other when A is 400m and B is 300m from the junction is 3.34 m/s.