Relative Motion in Two Dimensions
PHXI04:MOTION IN A PLANE

362081 100 \(m\) wide river is flowing with velocity 4 \(m\)/\(s\) and a man can swim in still water with velocity 5 \(m\)/\(s\). He wants to cross the river along shortest path. Find the direction in which the person should swim w.r.to river flow
supporting img

1 \(\frac{\pi }{2} + {\sin ^{ - 1}}\left( {\frac{4}{5}} \right)\)
2 \(\frac{\pi }{2} + {\cos ^{ - 1}}\left( {\frac{2}{5}} \right)\)
3 \(\frac{\pi }{2} + {\cos ^{ - 1}}\left( {\frac{3}{5}} \right)\)
4 \({\cos ^{ - 1}}\left( {\frac{4}{5}} \right)\)
PHXI04:MOTION IN A PLANE

362082 A steam boat goes across a lake and comes back \((i)\) on a quiet day when the water is still and \((ii)\) on a rough day when there is a uniform current so as to help the journey on wards and to impede the journey back. If the speed of the launch on both days was same, the time required for complete journey on the rough day, as compared to the quiet day will be

1 More
2 Less
3 Same
4 None of these
PHXI04:MOTION IN A PLANE

362083 A swimmer can swim in still water at a rate \(4.0\,km{\rm{/}}h\). If the swims in a river flowing at \(3.0\,km{\rm{/}}h\) and keeps his direction (with respect to water) perpendicular to the current, find his velocity with respect to the ground.

1 \(25\;\,\,km{\rm{/}}h\)
2 \(5\;\,\,km{\rm{/}}h\)
3 \(7\;\,\,km{\rm{/}}h\)
4 \(17.2\;\,\,km{\rm{/}}h\)
PHXI04:MOTION IN A PLANE

362084 The speed of a swimmer in still water is 20 \(m\)/\(s\). The speed of river water is 10 m/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 w.r.t. north is given by :

1 \(30^\circ \,\,{\mathop{\rm west}\nolimits} \)
2 \(0^\circ \,\,{\mathop{\rm west}\nolimits} \)
3 \(60^\circ \,\,{\mathop{\rm west}\nolimits} \)
4 \(45^\circ \,\,{\mathop{\rm west}\nolimits} \)
PHXI04:MOTION IN A PLANE

362081 100 \(m\) wide river is flowing with velocity 4 \(m\)/\(s\) and a man can swim in still water with velocity 5 \(m\)/\(s\). He wants to cross the river along shortest path. Find the direction in which the person should swim w.r.to river flow
supporting img

1 \(\frac{\pi }{2} + {\sin ^{ - 1}}\left( {\frac{4}{5}} \right)\)
2 \(\frac{\pi }{2} + {\cos ^{ - 1}}\left( {\frac{2}{5}} \right)\)
3 \(\frac{\pi }{2} + {\cos ^{ - 1}}\left( {\frac{3}{5}} \right)\)
4 \({\cos ^{ - 1}}\left( {\frac{4}{5}} \right)\)
PHXI04:MOTION IN A PLANE

362082 A steam boat goes across a lake and comes back \((i)\) on a quiet day when the water is still and \((ii)\) on a rough day when there is a uniform current so as to help the journey on wards and to impede the journey back. If the speed of the launch on both days was same, the time required for complete journey on the rough day, as compared to the quiet day will be

1 More
2 Less
3 Same
4 None of these
PHXI04:MOTION IN A PLANE

362083 A swimmer can swim in still water at a rate \(4.0\,km{\rm{/}}h\). If the swims in a river flowing at \(3.0\,km{\rm{/}}h\) and keeps his direction (with respect to water) perpendicular to the current, find his velocity with respect to the ground.

1 \(25\;\,\,km{\rm{/}}h\)
2 \(5\;\,\,km{\rm{/}}h\)
3 \(7\;\,\,km{\rm{/}}h\)
4 \(17.2\;\,\,km{\rm{/}}h\)
PHXI04:MOTION IN A PLANE

362084 The speed of a swimmer in still water is 20 \(m\)/\(s\). The speed of river water is 10 m/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 w.r.t. north is given by :

1 \(30^\circ \,\,{\mathop{\rm west}\nolimits} \)
2 \(0^\circ \,\,{\mathop{\rm west}\nolimits} \)
3 \(60^\circ \,\,{\mathop{\rm west}\nolimits} \)
4 \(45^\circ \,\,{\mathop{\rm west}\nolimits} \)
PHXI04:MOTION IN A PLANE

362081 100 \(m\) wide river is flowing with velocity 4 \(m\)/\(s\) and a man can swim in still water with velocity 5 \(m\)/\(s\). He wants to cross the river along shortest path. Find the direction in which the person should swim w.r.to river flow
supporting img

1 \(\frac{\pi }{2} + {\sin ^{ - 1}}\left( {\frac{4}{5}} \right)\)
2 \(\frac{\pi }{2} + {\cos ^{ - 1}}\left( {\frac{2}{5}} \right)\)
3 \(\frac{\pi }{2} + {\cos ^{ - 1}}\left( {\frac{3}{5}} \right)\)
4 \({\cos ^{ - 1}}\left( {\frac{4}{5}} \right)\)
PHXI04:MOTION IN A PLANE

362082 A steam boat goes across a lake and comes back \((i)\) on a quiet day when the water is still and \((ii)\) on a rough day when there is a uniform current so as to help the journey on wards and to impede the journey back. If the speed of the launch on both days was same, the time required for complete journey on the rough day, as compared to the quiet day will be

1 More
2 Less
3 Same
4 None of these
PHXI04:MOTION IN A PLANE

362083 A swimmer can swim in still water at a rate \(4.0\,km{\rm{/}}h\). If the swims in a river flowing at \(3.0\,km{\rm{/}}h\) and keeps his direction (with respect to water) perpendicular to the current, find his velocity with respect to the ground.

1 \(25\;\,\,km{\rm{/}}h\)
2 \(5\;\,\,km{\rm{/}}h\)
3 \(7\;\,\,km{\rm{/}}h\)
4 \(17.2\;\,\,km{\rm{/}}h\)
PHXI04:MOTION IN A PLANE

362084 The speed of a swimmer in still water is 20 \(m\)/\(s\). The speed of river water is 10 m/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 w.r.t. north is given by :

1 \(30^\circ \,\,{\mathop{\rm west}\nolimits} \)
2 \(0^\circ \,\,{\mathop{\rm west}\nolimits} \)
3 \(60^\circ \,\,{\mathop{\rm west}\nolimits} \)
4 \(45^\circ \,\,{\mathop{\rm west}\nolimits} \)
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PHXI04:MOTION IN A PLANE

362081 100 \(m\) wide river is flowing with velocity 4 \(m\)/\(s\) and a man can swim in still water with velocity 5 \(m\)/\(s\). He wants to cross the river along shortest path. Find the direction in which the person should swim w.r.to river flow
supporting img

1 \(\frac{\pi }{2} + {\sin ^{ - 1}}\left( {\frac{4}{5}} \right)\)
2 \(\frac{\pi }{2} + {\cos ^{ - 1}}\left( {\frac{2}{5}} \right)\)
3 \(\frac{\pi }{2} + {\cos ^{ - 1}}\left( {\frac{3}{5}} \right)\)
4 \({\cos ^{ - 1}}\left( {\frac{4}{5}} \right)\)
PHXI04:MOTION IN A PLANE

362082 A steam boat goes across a lake and comes back \((i)\) on a quiet day when the water is still and \((ii)\) on a rough day when there is a uniform current so as to help the journey on wards and to impede the journey back. If the speed of the launch on both days was same, the time required for complete journey on the rough day, as compared to the quiet day will be

1 More
2 Less
3 Same
4 None of these
PHXI04:MOTION IN A PLANE

362083 A swimmer can swim in still water at a rate \(4.0\,km{\rm{/}}h\). If the swims in a river flowing at \(3.0\,km{\rm{/}}h\) and keeps his direction (with respect to water) perpendicular to the current, find his velocity with respect to the ground.

1 \(25\;\,\,km{\rm{/}}h\)
2 \(5\;\,\,km{\rm{/}}h\)
3 \(7\;\,\,km{\rm{/}}h\)
4 \(17.2\;\,\,km{\rm{/}}h\)
PHXI04:MOTION IN A PLANE

362084 The speed of a swimmer in still water is 20 \(m\)/\(s\). The speed of river water is 10 m/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 w.r.t. north is given by :

1 \(30^\circ \,\,{\mathop{\rm west}\nolimits} \)
2 \(0^\circ \,\,{\mathop{\rm west}\nolimits} \)
3 \(60^\circ \,\,{\mathop{\rm west}\nolimits} \)
4 \(45^\circ \,\,{\mathop{\rm west}\nolimits} \)