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.Bullet one 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

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 velocty of train with respect to monkey
a. 5m/s
b -5 m/s
c. 15 m/s
d -15 m/s

7. find the velocty of ground with respect to monkey
a. 5 m/s
b. -5 m/s
c. 10 m/s
d. -10 m/s

C.Two particles start from the origin of the horizontal x-y plane.Particle A moves along +x axis with uniform velocity u.Particle B moves along -y axis with velocity u. i and j are the unit vectors along x and y direction

8. find the relative velocity of particle B wrt to A at time t
a -u(i+j)
b u(i+j)
c 0
d none of the above

9. find the relative velocity of particle A wrt to B at time t
a -u(i+j)
b u(i+j)
c 0
d none of the above

10. find the relative position vector of particle A wrt to B at time t
a -ut(i+j)
b ut(i+j)
c. 0
d. None of the above


Solutions

Detailed Solutions

Ans 1
Velocity of bullet w.rt to train=u
Velcity 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



Ans 4.
Velocity of bullet w.rt to train=-u
Velcity of train=v
velocity of car
Velocity of bullet w.rt to car=Velocity of bullet w.r.t earth -Velocity of car w.r.t earth
= v-u-w


Ans 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

Ans 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



Ans 8.

Velocity of A=ui
Velocity of B =-uj

Velocity of B w.r.t to A=Velocity of B-Velocity of A
=-u(i+j)

Ans 9

Velocity of A=ui
Velocity of B =-uj

Velocity of A w.r.t to B=Velocity of A-Velocity of B
=u(i+j)

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