Relative Velocity - UNSOLVED PRACTICE SET

Q7. Define relative velocity. Write the vector equation for the velocity of object A relative to object B.

Q8. A car is moving at 20 m/s and another car is moving at 15 m/s in the same direction. Calculate the velocity of the first car relative to the second car.

Q9. Rain is falling vertically at 8 m/s. A cyclist moves horizontally at 6 m/s. At what angle with the vertical should the cyclist hold his umbrella to protect himself from rain?

Q10. In a Delhi Metro train moving at 15 m/s, a passenger walks towards the front at 1 m/s relative to the train. What is the passenger's velocity relative to the platform? What if he walks towards the rear?

Q11. A boat can move at 5 m/s in still water. It is to cross a river flowing at 3 m/s. What should be the direction of the boat relative to the river flow so that it reaches the point directly opposite to the starting point?

Q12. Two particles are moving with velocities v₁ = 3i + 4j m/s and v₂ = 5i − 2j m/s. Calculate the velocity of particle 1 relative to particle 2.

Q13. Explain the concept of relative velocity with examples. Derive the general expression for relative velocity in two dimensions. Discuss the special cases:

(i) Two bodies moving in the same direction

(ii) Two bodies moving in opposite directions

(iii) Two bodies moving at right angles to each other

Q14. A river is 500 m wide and flows eastward at 2 m/s. A boat can move at 4 m/s in still water.

(a) If the boat heads directly north, calculate the time to cross the river and the downstream drift.

(b) In what direction should the boat be steered to reach a point directly north of the starting point? Calculate the time taken in this case.

(c) Calculate the minimum time to cross the river and the corresponding direction of steering.

Q15. Two trains, A and B, are moving on parallel tracks. Train A is 150 m long and moves at 20 m/s. Train B is 100 m long and moves at 15 m/s in the same direction.

(a) Calculate the time taken for Train A to completely overtake Train B.

(b) If the trains are moving in opposite directions, calculate the time taken to completely pass each other.

(c) A passenger in Train A throws a ball vertically upward at 10 m/s relative to the train. Describe the path of the ball as seen by an observer on the ground.

Q16. An aeroplane is flying horizontally at a height of 1960 m with a speed of 360 km/h. At a certain instant, it drops a relief package.

(a) Calculate the time taken for the package to reach the ground.

(b) Calculate the horizontal distance from the point of release to where the package lands.

(c) What is the velocity of the package relative to the aeroplane at the instant of release?

(d) What is the velocity of the package relative to the ground just before hitting the ground? (Take g = 9.8 m/s²)

Q17. A man standing on an open truck moving at 10 m/s in the rain holds his umbrella at 30° with the vertical to protect himself. When the truck stops, he has to hold the umbrella vertically.

(a) Calculate the velocity of rain with respect to the ground.

(b) Calculate the velocity of rain with respect to the truck when moving.

(c) Verify your answers using vector diagrams.

Q18. Two ships, A and B, are initially 10 km apart. Ship A moves north at 20 km/h and Ship B moves east at 15 km/h.

(a) Calculate the velocity of Ship A relative to Ship B.

(b) Calculate the initial distance of closest approach between the two ships.

(c) Calculate the time at which this closest approach occurs.

(d) Draw a diagram showing the positions and velocities of both ships.