Relative Velocity in 2D

Q. A particle $A$ is projected with an initial velocity of $60m/s$ at an angle ${30}^{\circ }$ to the horizontal. At the same time, a second particle $B$ is projected at an angle $\alpha$ to the horizontal with an initial speed of $50m/s$ from a point at a distance of $100m$ from $A$ as shown in the figure. If the particles collide in the air, find the angle of projection $\alpha$ of particle $B$.

1. ${30}^{\circ }$
2. ${60}^{\circ }$
3. $\sin {}^{-1}\left(\frac{3}{5}\right)$
4. $\cos {}^{-1}\left(\frac{3}{5}\right)$

Q. An aeroplane is flying at a constant horizontal velocity of 600 km/hr at an elevation of 6 km towards a point directly above the target on the earth's surface. At an appropriate time, the pilot releases a ball so that it strikes the target at the earth. The ball will appear to be falling

1. Vertically along a straight path as seen by an observer on the ground near the target
2. On a parabolic path as seen by an observer on the ground near the target
3. On a zig-zag path as seen by pilot in the plane
4. On a parabolic path as seen by pilot in the plane

Q.

A boy throws a ball upwards with velocity $v_0$ = 20 m/s . The wind imparts a horizontal acceleration of 4 m/$s^2$ to the left.

The angle $\theta$ at which the ball must be thrown so that the ball returns to the boy's hand is ( g = 10m/$s^2$ )

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2. 

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Q.

Two particles A and B are moving with uniform velocity as shown in the figure given below at t = 0.

What is the shortest distance between two particles?

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2. 

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Q.

An aero-plane pilot wishes to fly due west. A wind of 100 km/h is blowing toward the south. If the airspeed of the plane (its speed in still air) is 300 km/h, I which direction should the pilot head? What is the speed of the plane w.r.t. the ground?

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3. 
   
   

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Q.

A river is flowing with a speed of 1 km/hr. A swimmer wants to go to point 'C' starting from 'A'. He swims with a speed of 5 km/hr at an angle $\theta$ w.r.t the river flow. If AB = BC = 400 m. At what angle with river bank should swimmer swim?

1. $\theta ={45}^{\circ }$

2. $\theta ={60}^{\circ }$

3. $\theta ={37}^{\circ }$

4. $\theta ={53}^{\circ }$

Q.

A political party has to start its procession in an area where wind is blowing at a speed of 41.4 km/h and party flags on the vehicles are fluttering along north-east direction. If the procession starts with a speed of 40 km/h towards north, find the direction of flags on the vehicles.

1. south of east

2. north of east

3. north of east

4. south of east

Q.

Three particles A, B and C are situated at the vertices of an equilateral triangle ABC of side 'd' at t = 0. Each of the particles moves with constant speed v. A always has its velocity along AB, B along BC and C along CA. At what time will the particles meet each other?

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Q.

A river flows due south with a speed of 2.0 m/s. A man steers a motorboat across the river; his velocity relative to the water is 4 m/s due east. The river is 800 m wide. What is his velocity relative to the earth? Assume North as positive y-direction.

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Q.

A boat moves relative to water with a velocity 'v' which is n times less than the river flow velocity u. At what angle to the north direction must the boat move to minimize drifting if the river flows from west to east?

1. $\theta =si{n}^{-1}n$

2. $\theta =co{s}^{-1}\frac{1}{n}$

3. $\theta =si{n}^{-1}\frac{1}{n}$

4. $noneofthese$