### Relative velocity Conceptual questions

**A.** A gun is mounted on a train roof .Train is travelling with the velocity v in north direction.A car is also moving on a parallel track with train with velocity w in north direction.Two bullet are fired from the muzzle of the gun . Take north as positive and south as negative

**1.** Bullet one is fired in the north direction with the muzzle velocity $u$ . Find the velocity of the bullet as seen from the observer on the earth

a. $u+v$

b. $u-v$

c. $u$

d. $v$

**2.** find the velocity of the bullet as seen from the observer on the moving car

a. $u+v-w$

b. $u-v-w$

c. $u$

d. $v$

**3**.Second Bullet is fired in the south direction with the muzzle velocity $u$.Find the velocity of the bullet as seen from the observer on the earth

a. $u+v$

b. $v-u$

c. $u$

d. $v$

**4.**find the velocity of the second bullet as seen from the observer on the moving car

a. $u+v-w$

b. $v-u-w$

c. $u$

d. $v$

Check your Answers
**1.** Velocity of bullet w.rt to train=u

Velocity of train = v

Velocity of bullet w.rt to train=Velocity of bullet w.r.t earth -Velocity of train w.r.t earth

So Velocity of bullet w.r.t earth =Velocity of bullet w.rt to train+Velocity of train w.r.t earth

$=u+v$

**2.** Velocity of bullet w.r.t earth =u +v

Velocity of Car w.r.t earth =w

Velocity of bullet w.rt to car=Velocity of bullet w.r.t earth -Velocity of car w.r.t earth

$=u+v-w$

**3.** Velocity of bullet w.rt to train= -u

Velocity of train = v

Velocity of bullet w.rt to train=Velocity of bullet w.r.t earth -Velocity of train w.r.t earth

So Velocity of bullet w.r.t earth =Velocity of bullet w.rt to train+Velocity of train w.r.t earth

$=-u+v= v-v$

**4.** Velocity of bullet w.rt to train=-u

Velocity of train w.r.t earth =v

velocity of car w.r.t earth =w

Velocity of bullet w.rt to car=Velocity of bullet w.r.t earth -Velocity of car w.r.t earth

$= v-u-w$

**B.** A train is moving in the west direction with a velocity 15m/s.A monkey runs on the roof of the train against its motion with a velocity 5m/s with respect to train .Take the motion along west as positive

**5.**Velocity of train relative to its driver

a. 0

b. 15 m/s

c. -15 m/s

d. 20 m/s

**6.** What is the velocity of train with respect to monkey

a. 5m/s

b -5 m/s

c. 15 m/s

d -15 m/s

**7.** find the velocity of monkey with respect to ground

a. 5 m/s

b. -5 m/s

c. 10 m/s

d. -10 m/s

Check your Answers
**5.**

Velocity of train w.r.t to driver=Velocity of train w.r.t earth -Velocity of driver w.r.t earth

so =0

**6.**

Given

velocity of train = 15m/s

velocity of monkey w.r.t train=-5 m/s

Now velocity of monkey w.r.t train=-velocity of train w.r.t monkey

So velocity of train w.r.t monkey = 5 m/s

**7. **velocity of train = 15m/s

velocity of monkey w.r.t train=-5 m/s

velocity of monkey w.r.t train = velocity of monkey with respect to ground - velocity of train

-5 =velocity of monkey with respect to ground - 15

velocity of monkey with respect to ground =10 m/s