Two identical freight cars roll without friction (one at 1 m/s, the other at 2 m/s) toward each other on a level track. They collide, couple together, and roll away in the direction that .

They collide, couple together, and roll away in the direction that the 2m/s car was rolling in.

Explanation:

We should start off with stating that the conservation of momentum is used here.

Momentum = mass * speed

Since, mass of both freight cars is the same, the speed determines which has more momentum.

Thus, the momentum of the 2 m/s freight car is twice that of the 1 m/s freight car.

The final speed is calculated as below:

mass * (velocity of first freight car) + mass * (velocity of second freight car) = (mass of both freight cars) * final velocity

(m * V1) + (m * V2) = (2m * V)

Let's substitute the velocities 1m/s for the first car, and - 2m/s for the second. (since the second is opposite in direction)

We get:

solving this we get:

V = - 0.5 m/s

Thus we can see that both cars will roll away in the direction that the 2 m/s car was going in. (because of the negative sign in the answer)

the cost of running the bulbs is 11.25p

Explanation:

Given;

cost of running 1 kwh = 10 p

power of filament bulb, P = 60 W

power of the CFL bulb, P = 15 W

time of power consumption, t = 15 hours

Total Energy consumed;

E = (60W + 15W) x 15 hours

E = (75)(15)

E = 1125 Wh

E = 1.125 kWh

Cost of 1.125 kWh  =   1.125 x 10p

                               = 11.25p

Therefore, the cost of running the bulbs is 11.25p