Relative Velocity in Two Dimensions

Unspecified year 11 questions

1. A moves with $65 km/h$ while B is coming back of A with $80 km/h$. The relative velocity of B with respect to A is
2. A boat crosses a river with a velocity of $8 km/h$. If the resulting velocity of boat is $10 km/h$ then the velocity of river water is
3. A boat is moving with a velocity $3\hat{i} + 4\hat{j}$ with respect to ground. The water in the river is moving with a velocity $-3\hat{i} - 4\hat{j}$ with respect to ground. The relative velocity of the boat with respect to water is
4. A boat B is moving westwards with a speed of $20kmh^{-1}$ and a boat C 200 km south of B is moving norhtwards with a speed of $20kmh^{-1}$. The time after which the distance between then becomes shortest is
5. A boat B is moving upstream with velocity $3 m/s$ with respect to ground. An observer standing on boat observes that a swimmer S is crossing the river perpendicular If river flow velocity is $4 m/s$ and swion of motion of boat. of width 100 m in 50sec, then [add image]
6. If rain falls vertically with a velocity. $V_{r}$ and wind blows With a velocity $v_{w}$ from east to west, then a person standing on the roadside should hold the umbrella in the direction
7. If $V_{r}$ is the velocity of rain falling vertically and $V_{m}$ is the velocity of a man walking on a level road, and $\theta$ is the angle with vertical at which he should hold the umbrella to protect himself, than the relative velocity of rain w.r.t. the man is given by:
8. A river flow with a speed more than the maximum speed with which a person can swim in the still water. He intends to cross the river by shortest possible path (i.e., he wants to reach the point on the opposite bank which directly opposite to the starting point). Which of the following correct?
9. A person aiming to reach the exactly opposite point on the bank of a stream is swimming with a speed of $0.5 m/s$ at an angle of $120^{\circ}$ with the direction of flow of water. The speed of water in the stream is
10. A swimmer wants to cross a river straight. He swim at $5 km/hr$ in still water. A river 1 km wide flows at the rate of $3 km/hr$. Which of the following figure shows the correct direction for the swimmer along which he should strike? ($V_{s} \rightarrow$ velocity of swimmer, $V_{r} \rightarrow$ velocity of river, V $\rightarrow$ resultant velocity)
11. A boat which has a speed of $5 km h^{-1}$ in still water crosses a river of width 1 km along the shortest possible path in 15 minutes. The velocity of the river water is