02. Relative Velocity in Plane
Motion in Plane

143724 A man crosses a \(320 \quad m\) wide river perpendicular to the current in \(4 \mathbf{~ m i n}\). If in still water he can swim with a speed \(5 / 3\) times that of the current, then the speed of the current, in \(\mathbf{m m}^{-1}\) is

1 30
2 40
3 50
4 60
Motion in Plane

143725 Rain is falling at an angle of \(30^{\circ}\) from the vertical due to the wind with a speed of \(40 \mathrm{~m} / \mathrm{s}\). A car is travelling horizontally in the direction opposite to the wind, at a speed of \(40 \mathrm{~m} / \mathrm{s}\). At what angle from the vertical will it experience the rain falling from?

1 \(30^{\circ}\)
2 \(60^{\circ}\)
3 \(90^{\circ}\)
4 \(120^{\circ}\)
Motion in Plane

143726 Two cars \(A\) and \(B\) are moving with speeds \(v_{A}=\) \(120 \mathrm{~km} / \mathrm{h}\) and \(v_{B}=50 \mathrm{~km} / \mathrm{h}\) respectively in the directions as indicated by the arrow in the figure below. What is the relative speed of the car \(B\) with respect to car \(A\) ?

1 \(70 \mathrm{~km} / \mathrm{h}\)
2 \(120 \mathrm{~km} / \mathrm{h}\)
3 \(130 \mathrm{~km} / \mathrm{h}\)
4 \(170 \mathrm{~km} / \mathrm{h}\)
Motion in Plane

143727 A river \(200 \mathrm{~m}\) wide is flowing at a rate of 3.0 \(\mathrm{m} / \mathrm{s}\). A boat is sailing at a velocity of \(15 \mathrm{~m} / \mathrm{s}\) with respect to the water in a direction perpendicular to the river. How far from the point directly opposite to the starting point does the boat reach on the opposite bank?

1 \(25 \mathrm{~m}\)
2 \(60 \mathrm{~m}\)
3 \(40 \mathrm{~m}\)
4 \(50 \mathrm{~m}\)
Motion in Plane

143728 Rain is falling vertically with a speed of \(30 \mathrm{~m} / \mathrm{s}\). A man rides a bicycle with a speed of \(10 \mathrm{~m} / \mathrm{s}\) from East to West direction. At what the angle with the vertical, he sees the rain falling?

1 \(\tan ^{-1}\left(\frac{1}{3}\right)\) towards West
2 \(\tan ^{-1}(3)\) towards West
3 \(\tan ^{-1}\left(\frac{1}{3}\right)\) towards East
4 \(\tan ^{-1}(3)\) towards East
Motion in Plane

143724 A man crosses a \(320 \quad m\) wide river perpendicular to the current in \(4 \mathbf{~ m i n}\). If in still water he can swim with a speed \(5 / 3\) times that of the current, then the speed of the current, in \(\mathbf{m m}^{-1}\) is

1 30
2 40
3 50
4 60
Motion in Plane

143725 Rain is falling at an angle of \(30^{\circ}\) from the vertical due to the wind with a speed of \(40 \mathrm{~m} / \mathrm{s}\). A car is travelling horizontally in the direction opposite to the wind, at a speed of \(40 \mathrm{~m} / \mathrm{s}\). At what angle from the vertical will it experience the rain falling from?

1 \(30^{\circ}\)
2 \(60^{\circ}\)
3 \(90^{\circ}\)
4 \(120^{\circ}\)
Motion in Plane

143726 Two cars \(A\) and \(B\) are moving with speeds \(v_{A}=\) \(120 \mathrm{~km} / \mathrm{h}\) and \(v_{B}=50 \mathrm{~km} / \mathrm{h}\) respectively in the directions as indicated by the arrow in the figure below. What is the relative speed of the car \(B\) with respect to car \(A\) ?

1 \(70 \mathrm{~km} / \mathrm{h}\)
2 \(120 \mathrm{~km} / \mathrm{h}\)
3 \(130 \mathrm{~km} / \mathrm{h}\)
4 \(170 \mathrm{~km} / \mathrm{h}\)
Motion in Plane

143727 A river \(200 \mathrm{~m}\) wide is flowing at a rate of 3.0 \(\mathrm{m} / \mathrm{s}\). A boat is sailing at a velocity of \(15 \mathrm{~m} / \mathrm{s}\) with respect to the water in a direction perpendicular to the river. How far from the point directly opposite to the starting point does the boat reach on the opposite bank?

1 \(25 \mathrm{~m}\)
2 \(60 \mathrm{~m}\)
3 \(40 \mathrm{~m}\)
4 \(50 \mathrm{~m}\)
Motion in Plane

143728 Rain is falling vertically with a speed of \(30 \mathrm{~m} / \mathrm{s}\). A man rides a bicycle with a speed of \(10 \mathrm{~m} / \mathrm{s}\) from East to West direction. At what the angle with the vertical, he sees the rain falling?

1 \(\tan ^{-1}\left(\frac{1}{3}\right)\) towards West
2 \(\tan ^{-1}(3)\) towards West
3 \(\tan ^{-1}\left(\frac{1}{3}\right)\) towards East
4 \(\tan ^{-1}(3)\) towards East
Motion in Plane

143724 A man crosses a \(320 \quad m\) wide river perpendicular to the current in \(4 \mathbf{~ m i n}\). If in still water he can swim with a speed \(5 / 3\) times that of the current, then the speed of the current, in \(\mathbf{m m}^{-1}\) is

1 30
2 40
3 50
4 60
Motion in Plane

143725 Rain is falling at an angle of \(30^{\circ}\) from the vertical due to the wind with a speed of \(40 \mathrm{~m} / \mathrm{s}\). A car is travelling horizontally in the direction opposite to the wind, at a speed of \(40 \mathrm{~m} / \mathrm{s}\). At what angle from the vertical will it experience the rain falling from?

1 \(30^{\circ}\)
2 \(60^{\circ}\)
3 \(90^{\circ}\)
4 \(120^{\circ}\)
Motion in Plane

143726 Two cars \(A\) and \(B\) are moving with speeds \(v_{A}=\) \(120 \mathrm{~km} / \mathrm{h}\) and \(v_{B}=50 \mathrm{~km} / \mathrm{h}\) respectively in the directions as indicated by the arrow in the figure below. What is the relative speed of the car \(B\) with respect to car \(A\) ?

1 \(70 \mathrm{~km} / \mathrm{h}\)
2 \(120 \mathrm{~km} / \mathrm{h}\)
3 \(130 \mathrm{~km} / \mathrm{h}\)
4 \(170 \mathrm{~km} / \mathrm{h}\)
Motion in Plane

143727 A river \(200 \mathrm{~m}\) wide is flowing at a rate of 3.0 \(\mathrm{m} / \mathrm{s}\). A boat is sailing at a velocity of \(15 \mathrm{~m} / \mathrm{s}\) with respect to the water in a direction perpendicular to the river. How far from the point directly opposite to the starting point does the boat reach on the opposite bank?

1 \(25 \mathrm{~m}\)
2 \(60 \mathrm{~m}\)
3 \(40 \mathrm{~m}\)
4 \(50 \mathrm{~m}\)
Motion in Plane

143728 Rain is falling vertically with a speed of \(30 \mathrm{~m} / \mathrm{s}\). A man rides a bicycle with a speed of \(10 \mathrm{~m} / \mathrm{s}\) from East to West direction. At what the angle with the vertical, he sees the rain falling?

1 \(\tan ^{-1}\left(\frac{1}{3}\right)\) towards West
2 \(\tan ^{-1}(3)\) towards West
3 \(\tan ^{-1}\left(\frac{1}{3}\right)\) towards East
4 \(\tan ^{-1}(3)\) towards East
Motion in Plane

143724 A man crosses a \(320 \quad m\) wide river perpendicular to the current in \(4 \mathbf{~ m i n}\). If in still water he can swim with a speed \(5 / 3\) times that of the current, then the speed of the current, in \(\mathbf{m m}^{-1}\) is

1 30
2 40
3 50
4 60
Motion in Plane

143725 Rain is falling at an angle of \(30^{\circ}\) from the vertical due to the wind with a speed of \(40 \mathrm{~m} / \mathrm{s}\). A car is travelling horizontally in the direction opposite to the wind, at a speed of \(40 \mathrm{~m} / \mathrm{s}\). At what angle from the vertical will it experience the rain falling from?

1 \(30^{\circ}\)
2 \(60^{\circ}\)
3 \(90^{\circ}\)
4 \(120^{\circ}\)
Motion in Plane

143726 Two cars \(A\) and \(B\) are moving with speeds \(v_{A}=\) \(120 \mathrm{~km} / \mathrm{h}\) and \(v_{B}=50 \mathrm{~km} / \mathrm{h}\) respectively in the directions as indicated by the arrow in the figure below. What is the relative speed of the car \(B\) with respect to car \(A\) ?

1 \(70 \mathrm{~km} / \mathrm{h}\)
2 \(120 \mathrm{~km} / \mathrm{h}\)
3 \(130 \mathrm{~km} / \mathrm{h}\)
4 \(170 \mathrm{~km} / \mathrm{h}\)
Motion in Plane

143727 A river \(200 \mathrm{~m}\) wide is flowing at a rate of 3.0 \(\mathrm{m} / \mathrm{s}\). A boat is sailing at a velocity of \(15 \mathrm{~m} / \mathrm{s}\) with respect to the water in a direction perpendicular to the river. How far from the point directly opposite to the starting point does the boat reach on the opposite bank?

1 \(25 \mathrm{~m}\)
2 \(60 \mathrm{~m}\)
3 \(40 \mathrm{~m}\)
4 \(50 \mathrm{~m}\)
Motion in Plane

143728 Rain is falling vertically with a speed of \(30 \mathrm{~m} / \mathrm{s}\). A man rides a bicycle with a speed of \(10 \mathrm{~m} / \mathrm{s}\) from East to West direction. At what the angle with the vertical, he sees the rain falling?

1 \(\tan ^{-1}\left(\frac{1}{3}\right)\) towards West
2 \(\tan ^{-1}(3)\) towards West
3 \(\tan ^{-1}\left(\frac{1}{3}\right)\) towards East
4 \(\tan ^{-1}(3)\) towards East
Motion in Plane

143724 A man crosses a \(320 \quad m\) wide river perpendicular to the current in \(4 \mathbf{~ m i n}\). If in still water he can swim with a speed \(5 / 3\) times that of the current, then the speed of the current, in \(\mathbf{m m}^{-1}\) is

1 30
2 40
3 50
4 60
Motion in Plane

143725 Rain is falling at an angle of \(30^{\circ}\) from the vertical due to the wind with a speed of \(40 \mathrm{~m} / \mathrm{s}\). A car is travelling horizontally in the direction opposite to the wind, at a speed of \(40 \mathrm{~m} / \mathrm{s}\). At what angle from the vertical will it experience the rain falling from?

1 \(30^{\circ}\)
2 \(60^{\circ}\)
3 \(90^{\circ}\)
4 \(120^{\circ}\)
Motion in Plane

143726 Two cars \(A\) and \(B\) are moving with speeds \(v_{A}=\) \(120 \mathrm{~km} / \mathrm{h}\) and \(v_{B}=50 \mathrm{~km} / \mathrm{h}\) respectively in the directions as indicated by the arrow in the figure below. What is the relative speed of the car \(B\) with respect to car \(A\) ?

1 \(70 \mathrm{~km} / \mathrm{h}\)
2 \(120 \mathrm{~km} / \mathrm{h}\)
3 \(130 \mathrm{~km} / \mathrm{h}\)
4 \(170 \mathrm{~km} / \mathrm{h}\)
Motion in Plane

143727 A river \(200 \mathrm{~m}\) wide is flowing at a rate of 3.0 \(\mathrm{m} / \mathrm{s}\). A boat is sailing at a velocity of \(15 \mathrm{~m} / \mathrm{s}\) with respect to the water in a direction perpendicular to the river. How far from the point directly opposite to the starting point does the boat reach on the opposite bank?

1 \(25 \mathrm{~m}\)
2 \(60 \mathrm{~m}\)
3 \(40 \mathrm{~m}\)
4 \(50 \mathrm{~m}\)
Motion in Plane

143728 Rain is falling vertically with a speed of \(30 \mathrm{~m} / \mathrm{s}\). A man rides a bicycle with a speed of \(10 \mathrm{~m} / \mathrm{s}\) from East to West direction. At what the angle with the vertical, he sees the rain falling?

1 \(\tan ^{-1}\left(\frac{1}{3}\right)\) towards West
2 \(\tan ^{-1}(3)\) towards West
3 \(\tan ^{-1}\left(\frac{1}{3}\right)\) towards East
4 \(\tan ^{-1}(3)\) towards East