# Physics Questions and Answers – Motion in a Plane – Relative Velocity in Two Dimensions

«
»

This set of Physics online test focuses on “Motion in a Plane – Relative Velocity in Two Dimensions”.

1. The velocity of a car A is to 5î + 11ĵ. The velocity of another car B is 11î + 5ĵ. What is the relative velocity of B with respect to A?
a) 6î – 6ĵ
b) 11î + 5ĵ
c) 6î + 6ĵ
d) 5î + 5ĵ

Explanation: The formula for calculating relative velocity of a body with respect to another body is- relative velocity = Velocity vector of A – Velocity vector of B. Hence, here, the relative velocity = velocity of B – velocity of A = 6î – 6ĵ.

2. The velocity of a car A is to 5î. The velocity of another car B is 22î – 7ĵ. What is the relative velocity of A with respect to B?
a) -17î + 7ĵ
b) 7î + 17ĵ
c) -7î + 17ĵ
d) -17î + 7ĵ

Explanation: The formula for calculating relative velocity of a body with respect to another body is- relative velocity = Velocity vector of A – Velocity vector of B. Hence, here, the relative velocity = velocity of B – velocity of A = -17î + 7ĵ.

3. Velocity of a man is 25 units in the positive X direction and 75 units in negative Y direction starting from the origin. Velocity of a woman is 25 units in the positive Y direction and 75 units in the negative X direction starting from the origin. What is the relative velocity of the man with respect to the woman?
a) 100î – 100ĵ
b) 100î + 100ĵ
c) -100î – 100ĵ
d) 0î + 0ĵ

Explanation: The velocity of the man is 25î – 75ĵ and that of the woman is -75î + 25ĵ. Relative velocity = velocity of man – velocity of woman = 100î – 100ĵ.

4. Velocity of a dog is 15 units in the positive X direction and 3 units in positive Y direction starting from the origin. Velocity of a pig is 7 units in the positive Y direction and 17 units in the positive X direction starting from the origin. What is the relative velocity of the dog with respect to the pig?
a) -2î – 4ĵ
b) -3î – 2ĵ
c) -4î – 2ĵ
d) 7î + 4ĵ

Explanation: The velocity of the man is 15î+3ĵ and that of the woman is 17î + 7ĵ. Relative velocity = velocity of dog– velocity of pig = -2î – 4ĵ.

5. A body is moving with a constant velocity of 4î + 3ĵ, starting from the origin. What will be the position of the body after 10s?
a) 40î + 30ĵ
b) 30î + 40ĵ
c) 30î – 40ĵ
d) 40î – 30ĵ

Explanation: The body’s displacement is given by s = vt. The body starts from the origin hence, the total displacement is the final position of the body. Therefore, after putting in the values, we get, s = (4î + 3ĵ)*10 = 40î + 30ĵ.

6. A body is moving with a constant acceleration of 4î + 3ĵ, starting from the origin. What will be the position of the body after 5s?
a) 50î + 37.5ĵ
b) 37.5î + 50ĵ
c) 37.5î – 50ĵ
d) 50î – 37.5ĵ

Explanation: The body’s displacement is given by s = (1/2)at2. The body starts from the origin hence, the total displacement is the final position of the body. Therefore, after putting in the values, we get, s = (1/2)(4î + 3ĵ)*52 = 50î + 37.5ĵ.

7. A body is moving with a constant acceleration of 11î + 2ĵ, starting from î + ĵ. What will be the position of the body after 10s?
a) 551î + 101ĵ
b) 550î + 100ĵ
c) 100î – 550ĵ
d) 550î – 550ĵ

Explanation: The body’s displacement is given by s = (1/2)at2. Therefore, after putting in the values, we get, s = (1/2)(11î + 2ĵ)*102 = 550î + 100ĵ. The body initially starts from î + ĵ. Hence, the final position is = initial position + displacement = 551î + 101ĵ. 