02. Relative Velocity in Plane
Motion in Plane

143711 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 \(-3 \hat{\mathbf{i}}-4 \hat{\mathbf{j}}\) w.r.t. ground.
The relative velocity of boat w.r.t. water is

1 \(5 \hat{i}+6 \hat{j}\)
2 \(6 \hat{\mathrm{i}}+8 \hat{\mathrm{j}}\)
3 \(6 \hat{i}+8 \hat{k}\)
4 \(5 \hat{\mathrm{j}}-6 \hat{\mathrm{k}}\)
Motion in Plane

143712 A boat which has a speed of \(13 \mathrm{~km} / \mathrm{h}\) in still water, crosses a river of width \(1 \mathrm{~km}\) along the shortest possible path in 12 minute. the velocity of the river water in \(\mathrm{km} / \mathrm{h}\) is:

1 12
2 10
3 8
4 6
Motion in Plane

143713 A gun mounted on the top of a moving truck is aimed in the backward direction at an angle of \(30^{\circ}\) to the vertical. If the muzzle velocity of the gun is \(4 \mathrm{~m} / \mathrm{s}\), the value of the speed of the truck that will make the bullet come out vertically is :

1 \(1 \mathrm{~m} / \mathrm{s}\)
2 \(\frac{\sqrt{3}}{2} \mathrm{~m} / \mathrm{s}\)
3 \(0.5 \mathrm{~m} / \mathrm{s}\)
4 \(2 \mathrm{~m} / \mathrm{s}\)
Motion in Plane

143714 A person swims in a river aiming to reach exactly on the opposite point on the bank of a river. His speed of swimming is \(0.5 \mathrm{~m} / \mathrm{s}\) at an angle of \(120^{\circ}\) with the direction of flow of water. The speed of water is

1 \(1.0 \mathrm{~m} / \mathrm{s}\)
2 \(0.5 \mathrm{~m} / \mathrm{s}\)
3 \(0.25 \mathrm{~m} / \mathrm{s}\)
4 \(0.43 \mathrm{~m} / \mathrm{s}\)
Motion in Plane

143715 A rain drop of radius \(0.3 \mathrm{~mm}\) has a terminal velocity in air is \(1 \mathrm{~m} / \mathrm{s}\). The viscosity of air is \(8 \times\) \(10^{-5}\) poise. The viscous force on it is

1 \(45.2 \times 10^{-4}\) dyne
2 \(101.73 \times 10^{-5}\) dyne
3 \(16.95 \times 10^{-4}\) dyne
4 \(16.95 \times 10^{-5}\) dyne
Motion in Plane

143711 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 \(-3 \hat{\mathbf{i}}-4 \hat{\mathbf{j}}\) w.r.t. ground.
The relative velocity of boat w.r.t. water is

1 \(5 \hat{i}+6 \hat{j}\)
2 \(6 \hat{\mathrm{i}}+8 \hat{\mathrm{j}}\)
3 \(6 \hat{i}+8 \hat{k}\)
4 \(5 \hat{\mathrm{j}}-6 \hat{\mathrm{k}}\)
Motion in Plane

143712 A boat which has a speed of \(13 \mathrm{~km} / \mathrm{h}\) in still water, crosses a river of width \(1 \mathrm{~km}\) along the shortest possible path in 12 minute. the velocity of the river water in \(\mathrm{km} / \mathrm{h}\) is:

1 12
2 10
3 8
4 6
Motion in Plane

143713 A gun mounted on the top of a moving truck is aimed in the backward direction at an angle of \(30^{\circ}\) to the vertical. If the muzzle velocity of the gun is \(4 \mathrm{~m} / \mathrm{s}\), the value of the speed of the truck that will make the bullet come out vertically is :

1 \(1 \mathrm{~m} / \mathrm{s}\)
2 \(\frac{\sqrt{3}}{2} \mathrm{~m} / \mathrm{s}\)
3 \(0.5 \mathrm{~m} / \mathrm{s}\)
4 \(2 \mathrm{~m} / \mathrm{s}\)
Motion in Plane

143714 A person swims in a river aiming to reach exactly on the opposite point on the bank of a river. His speed of swimming is \(0.5 \mathrm{~m} / \mathrm{s}\) at an angle of \(120^{\circ}\) with the direction of flow of water. The speed of water is

1 \(1.0 \mathrm{~m} / \mathrm{s}\)
2 \(0.5 \mathrm{~m} / \mathrm{s}\)
3 \(0.25 \mathrm{~m} / \mathrm{s}\)
4 \(0.43 \mathrm{~m} / \mathrm{s}\)
Motion in Plane

143715 A rain drop of radius \(0.3 \mathrm{~mm}\) has a terminal velocity in air is \(1 \mathrm{~m} / \mathrm{s}\). The viscosity of air is \(8 \times\) \(10^{-5}\) poise. The viscous force on it is

1 \(45.2 \times 10^{-4}\) dyne
2 \(101.73 \times 10^{-5}\) dyne
3 \(16.95 \times 10^{-4}\) dyne
4 \(16.95 \times 10^{-5}\) dyne
Motion in Plane

143711 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 \(-3 \hat{\mathbf{i}}-4 \hat{\mathbf{j}}\) w.r.t. ground.
The relative velocity of boat w.r.t. water is

1 \(5 \hat{i}+6 \hat{j}\)
2 \(6 \hat{\mathrm{i}}+8 \hat{\mathrm{j}}\)
3 \(6 \hat{i}+8 \hat{k}\)
4 \(5 \hat{\mathrm{j}}-6 \hat{\mathrm{k}}\)
Motion in Plane

143712 A boat which has a speed of \(13 \mathrm{~km} / \mathrm{h}\) in still water, crosses a river of width \(1 \mathrm{~km}\) along the shortest possible path in 12 minute. the velocity of the river water in \(\mathrm{km} / \mathrm{h}\) is:

1 12
2 10
3 8
4 6
Motion in Plane

143713 A gun mounted on the top of a moving truck is aimed in the backward direction at an angle of \(30^{\circ}\) to the vertical. If the muzzle velocity of the gun is \(4 \mathrm{~m} / \mathrm{s}\), the value of the speed of the truck that will make the bullet come out vertically is :

1 \(1 \mathrm{~m} / \mathrm{s}\)
2 \(\frac{\sqrt{3}}{2} \mathrm{~m} / \mathrm{s}\)
3 \(0.5 \mathrm{~m} / \mathrm{s}\)
4 \(2 \mathrm{~m} / \mathrm{s}\)
Motion in Plane

143714 A person swims in a river aiming to reach exactly on the opposite point on the bank of a river. His speed of swimming is \(0.5 \mathrm{~m} / \mathrm{s}\) at an angle of \(120^{\circ}\) with the direction of flow of water. The speed of water is

1 \(1.0 \mathrm{~m} / \mathrm{s}\)
2 \(0.5 \mathrm{~m} / \mathrm{s}\)
3 \(0.25 \mathrm{~m} / \mathrm{s}\)
4 \(0.43 \mathrm{~m} / \mathrm{s}\)
Motion in Plane

143715 A rain drop of radius \(0.3 \mathrm{~mm}\) has a terminal velocity in air is \(1 \mathrm{~m} / \mathrm{s}\). The viscosity of air is \(8 \times\) \(10^{-5}\) poise. The viscous force on it is

1 \(45.2 \times 10^{-4}\) dyne
2 \(101.73 \times 10^{-5}\) dyne
3 \(16.95 \times 10^{-4}\) dyne
4 \(16.95 \times 10^{-5}\) dyne
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Motion in Plane

143711 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 \(-3 \hat{\mathbf{i}}-4 \hat{\mathbf{j}}\) w.r.t. ground.
The relative velocity of boat w.r.t. water is

1 \(5 \hat{i}+6 \hat{j}\)
2 \(6 \hat{\mathrm{i}}+8 \hat{\mathrm{j}}\)
3 \(6 \hat{i}+8 \hat{k}\)
4 \(5 \hat{\mathrm{j}}-6 \hat{\mathrm{k}}\)
Motion in Plane

143712 A boat which has a speed of \(13 \mathrm{~km} / \mathrm{h}\) in still water, crosses a river of width \(1 \mathrm{~km}\) along the shortest possible path in 12 minute. the velocity of the river water in \(\mathrm{km} / \mathrm{h}\) is:

1 12
2 10
3 8
4 6
Motion in Plane

143713 A gun mounted on the top of a moving truck is aimed in the backward direction at an angle of \(30^{\circ}\) to the vertical. If the muzzle velocity of the gun is \(4 \mathrm{~m} / \mathrm{s}\), the value of the speed of the truck that will make the bullet come out vertically is :

1 \(1 \mathrm{~m} / \mathrm{s}\)
2 \(\frac{\sqrt{3}}{2} \mathrm{~m} / \mathrm{s}\)
3 \(0.5 \mathrm{~m} / \mathrm{s}\)
4 \(2 \mathrm{~m} / \mathrm{s}\)
Motion in Plane

143714 A person swims in a river aiming to reach exactly on the opposite point on the bank of a river. His speed of swimming is \(0.5 \mathrm{~m} / \mathrm{s}\) at an angle of \(120^{\circ}\) with the direction of flow of water. The speed of water is

1 \(1.0 \mathrm{~m} / \mathrm{s}\)
2 \(0.5 \mathrm{~m} / \mathrm{s}\)
3 \(0.25 \mathrm{~m} / \mathrm{s}\)
4 \(0.43 \mathrm{~m} / \mathrm{s}\)
Motion in Plane

143715 A rain drop of radius \(0.3 \mathrm{~mm}\) has a terminal velocity in air is \(1 \mathrm{~m} / \mathrm{s}\). The viscosity of air is \(8 \times\) \(10^{-5}\) poise. The viscous force on it is

1 \(45.2 \times 10^{-4}\) dyne
2 \(101.73 \times 10^{-5}\) dyne
3 \(16.95 \times 10^{-4}\) dyne
4 \(16.95 \times 10^{-5}\) dyne
Motion in Plane

143711 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 \(-3 \hat{\mathbf{i}}-4 \hat{\mathbf{j}}\) w.r.t. ground.
The relative velocity of boat w.r.t. water is

1 \(5 \hat{i}+6 \hat{j}\)
2 \(6 \hat{\mathrm{i}}+8 \hat{\mathrm{j}}\)
3 \(6 \hat{i}+8 \hat{k}\)
4 \(5 \hat{\mathrm{j}}-6 \hat{\mathrm{k}}\)
Motion in Plane

143712 A boat which has a speed of \(13 \mathrm{~km} / \mathrm{h}\) in still water, crosses a river of width \(1 \mathrm{~km}\) along the shortest possible path in 12 minute. the velocity of the river water in \(\mathrm{km} / \mathrm{h}\) is:

1 12
2 10
3 8
4 6
Motion in Plane

143713 A gun mounted on the top of a moving truck is aimed in the backward direction at an angle of \(30^{\circ}\) to the vertical. If the muzzle velocity of the gun is \(4 \mathrm{~m} / \mathrm{s}\), the value of the speed of the truck that will make the bullet come out vertically is :

1 \(1 \mathrm{~m} / \mathrm{s}\)
2 \(\frac{\sqrt{3}}{2} \mathrm{~m} / \mathrm{s}\)
3 \(0.5 \mathrm{~m} / \mathrm{s}\)
4 \(2 \mathrm{~m} / \mathrm{s}\)
Motion in Plane

143714 A person swims in a river aiming to reach exactly on the opposite point on the bank of a river. His speed of swimming is \(0.5 \mathrm{~m} / \mathrm{s}\) at an angle of \(120^{\circ}\) with the direction of flow of water. The speed of water is

1 \(1.0 \mathrm{~m} / \mathrm{s}\)
2 \(0.5 \mathrm{~m} / \mathrm{s}\)
3 \(0.25 \mathrm{~m} / \mathrm{s}\)
4 \(0.43 \mathrm{~m} / \mathrm{s}\)
Motion in Plane

143715 A rain drop of radius \(0.3 \mathrm{~mm}\) has a terminal velocity in air is \(1 \mathrm{~m} / \mathrm{s}\). The viscosity of air is \(8 \times\) \(10^{-5}\) poise. The viscous force on it is

1 \(45.2 \times 10^{-4}\) dyne
2 \(101.73 \times 10^{-5}\) dyne
3 \(16.95 \times 10^{-4}\) dyne
4 \(16.95 \times 10^{-5}\) dyne