Relative Velocity in 2D

Q.

A person is swimming with a speed of $10\raisebox{1ex}{$m$}\!\left/ \!\raisebox{-1ex}{$s$}\right.$ at an angle of ${120}^o$ with the flow and reaches to a point directly opposite on the other side of the river. Then the speed of the flow is$‘x’\raisebox{1ex}{$m$}\!\left/ \!\raisebox{-1ex}{$s$}\right.$. The value of $‘x’$ to the nearest integer is _____.

Q. 2019-8-35 A Swimmer reaches the other bank of a flowingriver exactly opposite to the starting point. If he wasswimming at 2 km/hr while maintaining 150^° withthe flow, then time taken by him to cross the river1 km wide isw(1) 30 min(2) 1 hr(3) 2 hrs(4) 20 min/8

Q.

A boy throw 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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Q. A person , reaches a poimt directly opposite on the other bank of a flowing river , while swimming at a speed of 5m/s at an angle of 120^° with the flow .the speed of the flow must

Q. a particle is projected from ground at angle theta with horizontal with speed u the ratio of radius of curvature of its trajectory at point of projection to radius of curvature at max height is

Q. In older times the people used to think that the earth was flat Imagione that the earth is indeed not a sphere of radius R but an infinite plane of thickness H.what value of H is needed to allow the same gravitational acceleration to be exprienced as on the actual surface of the eart

Q. The speed of a swimmer in still water is $20m/s$. The speed of river water is $10m/s$ and is flowing due east. If he is standing on the south bank and wishes to cross the river along the shortest path, the angle at which he should make his strokes with respect to the north, is given by

1. $30°$ west
2. $0°$
3. $60°$ west
4. $45°$ west

Q. A person can swim in still water at 5m/s. How much time will he take to move a distance of 120m in stream of water flowing at 1m/s up stream and downstream respectively.

Q. he equation of trajectory of a projectile is given as2y=2xThe maximum height of projectile is2(Symbols have usual meanings and Sl unit)15(1) 4 m(2) 1 mta 2 m(4) 10 m

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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Q. In two seperate collisions, the coefficient of restitutions e_1 and e_2 are in the ratio 3:1. In the first collision the relative velocity of approach is twice the relative velocity of seperation. Then, the ratio between the relative velocity of aproach and relative velocity of seperation in second collision is (1) 1:6 (2) 2:3 (3) 3:2 (4) 6:1

Q. 10.: A launch takes 3 hrs to go downstream from point A to B and 6hrs to come back to A from B. The time taken by the launch to cover the same distance downstream when its engine cutoff is?

Q. 143.A projectile is fired with velocity u at entrance A of a horizontal tunnel of length L and height H. The minimum value of u for which projectile will reach at the other end of the tunnel without touching the top of the tunnel is

Q. The velocity at maximum height of projectile is root 3 by 2 times its initial velocity of projectile (u) . Its range on horizontal plane is

Q. A projectile is fired horizontally from a height of19.62 cm from the ground and reaches the groundat a horizontal distance of 49 m. The initial velocityis approximately(1) 20.1 m/s(2) 24.52 m/s(3) 28.32 m/s(4) 30.49 m/sian

Q. a bullet loses 1\n th of its velocity while penetrating a distance x into the target the further distance travelled before coming rest

Q.

A projectile is fired horizontally from a gun that is 45.0 m above flat ground, it emerges from the gun with a speed of 500 m/s. (take, g = $-10m/s^2$)

Column - I Column - II

(i) Time of flight of Projectile in s (x) 3

(ii) Horizontal distance covered by projectile in m (y) 30

(iii) Magnitude of vertical component of velocity in m/s as it strikes ground(z) 1500

1. (i) - (x); (ii) - (z); (iii) - (y)

2. (i) - (y); (ii) - (x); (iii) - (z)

3. (i) - (x); (ii) - (y); (iii) - (z)

4. (i) - (z); (ii) - (x); (iii) - (y)

Q.

A bird is flying due east with a velocity of 4 m/s. The wind starts to blow with a velocity of 3 m/s due north. What is the magnitude of relative velocity of bird w.r.t. wind? Find out the angle it makes with the x-axis?

1. 7m/s, $ta{n}^{-1}\left(\frac{3}{4}\right)$

2. 7 m/s, $ta{n}^{-1}\left(\frac{4}{3}\right)$

3. 5 m/s, $ta{n}^{-1}\left(\frac{3}{4}\right)$

4. 5 m/s, $ta{n}^{-1}\left(\frac{4}{3}\right)$

Q.

A ball is shot vertically upward from the surface of another planet. A plot of 'y' versus 't' for the ball is shown in figure where y is the height of the ball above its starting point and t = 0 at the instant the ball is shot. The figure's vertical scaling is set by $y_s$ = 30.0 m. What are the magnitudes of (a) the free-fall acceleration on the planet and (b) the initial velocity of the ball?

1. a = - 8 m/, u = + 20 m/s

2. a = 8 m/, u = + 20 m/s

3. a = - g m/, u = + 22.5 m/s

4. a = - 10/, u = + 25 m/s

Q. rain drops are falling with the velocity of v=4i-4j m/s. if a man is walking in a horizontal road with a velocity of i m/s along with an umbrella then the direction of umbrella to avoid rain

Q.

A man running on a horizontal road at 8 km/h finds the rain falling vertically. He increases his speed to 12 km/h and finds that the drops make angle ${30}^{\circ }$ with the vertical. Find the speed and direction of the rain with respect to the road.

1. $v_{rain}=4\sqrt{7}$ km/hr

   $\alpha =ta{n}^{-1}\left(\frac{\sqrt{3}}{2}\right)$

2. $v_{rain}=5$ km/hr

   $\alpha =co{t}^{-1}\left(\frac{\sqrt{3}}{2}\right)$

3. $v_{rain}=4\sqrt{7}$ km/hr

   $\alpha =ta{n}^{-1}\left(\frac{\sqrt{3}}{2}\right)$

4. $v_{rain}=4\sqrt{\frac{13}{3}}$ km/hr

   $\alpha =ta{n}^{-1}\left(\frac{2}{\sqrt{3}}\right)$

Q.

A motorboat going downstream overcame a raft at a point A; t = 60 minutes later, it turned back and after some time passed the raft at a distance l = 6.0 km from the point A. Find the flow velocity assuming the duty of the engine to be constant.

1. Data insufficient

2. 1 km/hr

3. 3 km/hr

4. 6 km/hr

Q.

A man wants to swim across a river from A to B and back from B to A always following line AB. The distance S between points A and B is S. The velocity of the river current v is constant over the entire width of the river. The line AB makes an angle $\alpha$ with the direction of current. Let the man travel with velocity u and at angle $\beta$ to the line AB. Find time 't' by which he will be back.

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Q. A particle $A$ starts from rest and moves with an acceleration of $5{\text{m/s}}^2$ due East while another particle $B$ moves with a constant velocity of $5\text{m/s}$ due North from the same position. Then the magnitude of relative position of $A$ w.r.t $B$ at 2 second is

1. $10\text{m}$
2. $10\sqrt{2}\text{m}$
3. $200\text{m}$
4. $\frac{10}{\sqrt{2}}\text{m}$

Q. Two particles A and B, move with constant velocities o V1 and v2. At the initial moment their position vectors are r1 and r2 respectively. The condition for particles A and B for their collision is:

Q. A boat takes $t_1$ time while going downstream between two fixed points $A$ and $B$, and takes $t_2$ time while going upstream through the same distance. If river does not flow, then the time taken by the boat to cover the same distance is

1. $t=\frac{2t_1{t}_2}{t_1+t_2}$
2. $t=\frac{t_1{t}_2}{t_1+t_2}$
3. $t=\frac{2t_2}{t_1+t_2}$
4. $t=\frac{2t_1}{t_1+t_2}$

Q. A cricket fielder can throw the cricket ball with a speed vo. If he throws the ball while running with speed u at an angle θ to the horizontal, find (a) the effective angle to the horizontal at which the ball is projected in air as seen by a spectator. (b) what will be time of flight? (c) what is the distance (horizontal range) from the point of projection at which the ball will land?

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. $\theta =ta{n}^{-1}\left(3\right)$ south of east

2. $\theta =ta{n}^{-1}\left(\frac{1}{3}\right)$ north of east

3. $\theta =ta{n}^{-1}\left(\frac{1}{3}\right)$ south of east

4. $\theta =ta{n}^{-1}\left(3\right)$ north of east

Q. A boat going downstream crosses a float at a point A. t1 minutes later the boat reverses its direction and in the next t2 minutes it crosses the float at a dis†an ce L from the point A. The velocity of the river i

Q. A cart is moving horizontally along a staight line with a constant speed $30\text{m/s}$. A bullet is to be fired vertically upwards from the moving cart in such a way that it returns to the cart at the same point from where it was fired, after the cart has moved $80\text{m}$. At what speed (relative to the cart), the bullet must be fired ? Take $g=10{\text{m/s}}^2$.

1. $10\text{m/s}$
2. $10\sqrt{8}\text{m/s}$
3. $\frac{40}{3}\text{m/s}$
4. $\frac{16}{\sqrt{3}}\text{m/s}$