02. Relative Velocity in Plane
Motion in Plane

143742 The speed of a boat is \(5 \mathrm{~km} / \mathrm{h}\) in still water. It crosses a river of width \(1.0 \mathrm{~km}\) along the shortest possible path in \(15 \mathrm{~min}\). The velocity of the river water is (in \(\mathrm{km} / \mathrm{h}\) )

1 5
2 1
3 3
4 4
Motion in Plane

143743 The speed of a swimmer in still water is \(20 \mathrm{~m} / \mathrm{s}\). The speed of river water is \(10 \mathrm{~m} / \mathrm{s}\) 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 \(0^{\circ}\)
2 \(60^{\circ}\) west
3 \(45^{\circ}\) west
4 \(30^{\circ}\) west
Motion in Plane

143744 A ship A is moving Westwards with a speed of \(10 \mathrm{~km} \mathrm{~h}^{-1}\) and a ship \(B 100 \mathrm{~km}\) South of \(A\), is moving Northwards with a speed of \(10 \mathrm{kmh}^{-1}\). The time after which the distance between them becomes shortest is

1 \(0 \mathrm{~h}\)
2 \(5 \mathrm{~h}\)
3 \(10 \sqrt{2} \mathrm{~h}\)
4 \(10 \sqrt{2} \mathrm{~h}\)
Motion in Plane

143745 A metro train starts from rest and in 5 sec achieves \(108 \mathrm{~km} / \mathrm{h}\). After that it moves with constant velocity and comes to rest after travelling \(45 \mathrm{~m}\) with uniform retardation. If total distance travelled is \(395 \mathrm{~m}\), find total time of travelling.

1 \(12.2 \mathrm{~s}\)
2 \(15.3 \mathrm{~s}\)
3 \(9 \mathrm{~s}\)
4 \(17.2 \mathrm{~s}\)
Motion in Plane

143746 A river is flowing from west to east with a speed of \(5 \mathrm{~m} / \mathrm{min}\). A man can swim in still water with a velocity \(10 \mathrm{~m} / \mathrm{min}\). In which direction should the man swim so, as to take the shortest possible path to go to the south?

1 \(30^{\circ}\) east of south
2 \(60^{\circ}\) east of south
3 \(60^{\circ}\) west of south
4 \(30^{\circ}\) west of south
Motion in Plane

143742 The speed of a boat is \(5 \mathrm{~km} / \mathrm{h}\) in still water. It crosses a river of width \(1.0 \mathrm{~km}\) along the shortest possible path in \(15 \mathrm{~min}\). The velocity of the river water is (in \(\mathrm{km} / \mathrm{h}\) )

1 5
2 1
3 3
4 4
Motion in Plane

143743 The speed of a swimmer in still water is \(20 \mathrm{~m} / \mathrm{s}\). The speed of river water is \(10 \mathrm{~m} / \mathrm{s}\) 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 \(0^{\circ}\)
2 \(60^{\circ}\) west
3 \(45^{\circ}\) west
4 \(30^{\circ}\) west
Motion in Plane

143744 A ship A is moving Westwards with a speed of \(10 \mathrm{~km} \mathrm{~h}^{-1}\) and a ship \(B 100 \mathrm{~km}\) South of \(A\), is moving Northwards with a speed of \(10 \mathrm{kmh}^{-1}\). The time after which the distance between them becomes shortest is

1 \(0 \mathrm{~h}\)
2 \(5 \mathrm{~h}\)
3 \(10 \sqrt{2} \mathrm{~h}\)
4 \(10 \sqrt{2} \mathrm{~h}\)
Motion in Plane

143745 A metro train starts from rest and in 5 sec achieves \(108 \mathrm{~km} / \mathrm{h}\). After that it moves with constant velocity and comes to rest after travelling \(45 \mathrm{~m}\) with uniform retardation. If total distance travelled is \(395 \mathrm{~m}\), find total time of travelling.

1 \(12.2 \mathrm{~s}\)
2 \(15.3 \mathrm{~s}\)
3 \(9 \mathrm{~s}\)
4 \(17.2 \mathrm{~s}\)
Motion in Plane

143746 A river is flowing from west to east with a speed of \(5 \mathrm{~m} / \mathrm{min}\). A man can swim in still water with a velocity \(10 \mathrm{~m} / \mathrm{min}\). In which direction should the man swim so, as to take the shortest possible path to go to the south?

1 \(30^{\circ}\) east of south
2 \(60^{\circ}\) east of south
3 \(60^{\circ}\) west of south
4 \(30^{\circ}\) west of south
Motion in Plane

143742 The speed of a boat is \(5 \mathrm{~km} / \mathrm{h}\) in still water. It crosses a river of width \(1.0 \mathrm{~km}\) along the shortest possible path in \(15 \mathrm{~min}\). The velocity of the river water is (in \(\mathrm{km} / \mathrm{h}\) )

1 5
2 1
3 3
4 4
Motion in Plane

143743 The speed of a swimmer in still water is \(20 \mathrm{~m} / \mathrm{s}\). The speed of river water is \(10 \mathrm{~m} / \mathrm{s}\) 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 \(0^{\circ}\)
2 \(60^{\circ}\) west
3 \(45^{\circ}\) west
4 \(30^{\circ}\) west
Motion in Plane

143744 A ship A is moving Westwards with a speed of \(10 \mathrm{~km} \mathrm{~h}^{-1}\) and a ship \(B 100 \mathrm{~km}\) South of \(A\), is moving Northwards with a speed of \(10 \mathrm{kmh}^{-1}\). The time after which the distance between them becomes shortest is

1 \(0 \mathrm{~h}\)
2 \(5 \mathrm{~h}\)
3 \(10 \sqrt{2} \mathrm{~h}\)
4 \(10 \sqrt{2} \mathrm{~h}\)
Motion in Plane

143745 A metro train starts from rest and in 5 sec achieves \(108 \mathrm{~km} / \mathrm{h}\). After that it moves with constant velocity and comes to rest after travelling \(45 \mathrm{~m}\) with uniform retardation. If total distance travelled is \(395 \mathrm{~m}\), find total time of travelling.

1 \(12.2 \mathrm{~s}\)
2 \(15.3 \mathrm{~s}\)
3 \(9 \mathrm{~s}\)
4 \(17.2 \mathrm{~s}\)
Motion in Plane

143746 A river is flowing from west to east with a speed of \(5 \mathrm{~m} / \mathrm{min}\). A man can swim in still water with a velocity \(10 \mathrm{~m} / \mathrm{min}\). In which direction should the man swim so, as to take the shortest possible path to go to the south?

1 \(30^{\circ}\) east of south
2 \(60^{\circ}\) east of south
3 \(60^{\circ}\) west of south
4 \(30^{\circ}\) west of south
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Motion in Plane

143742 The speed of a boat is \(5 \mathrm{~km} / \mathrm{h}\) in still water. It crosses a river of width \(1.0 \mathrm{~km}\) along the shortest possible path in \(15 \mathrm{~min}\). The velocity of the river water is (in \(\mathrm{km} / \mathrm{h}\) )

1 5
2 1
3 3
4 4
Motion in Plane

143743 The speed of a swimmer in still water is \(20 \mathrm{~m} / \mathrm{s}\). The speed of river water is \(10 \mathrm{~m} / \mathrm{s}\) 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 \(0^{\circ}\)
2 \(60^{\circ}\) west
3 \(45^{\circ}\) west
4 \(30^{\circ}\) west
Motion in Plane

143744 A ship A is moving Westwards with a speed of \(10 \mathrm{~km} \mathrm{~h}^{-1}\) and a ship \(B 100 \mathrm{~km}\) South of \(A\), is moving Northwards with a speed of \(10 \mathrm{kmh}^{-1}\). The time after which the distance between them becomes shortest is

1 \(0 \mathrm{~h}\)
2 \(5 \mathrm{~h}\)
3 \(10 \sqrt{2} \mathrm{~h}\)
4 \(10 \sqrt{2} \mathrm{~h}\)
Motion in Plane

143745 A metro train starts from rest and in 5 sec achieves \(108 \mathrm{~km} / \mathrm{h}\). After that it moves with constant velocity and comes to rest after travelling \(45 \mathrm{~m}\) with uniform retardation. If total distance travelled is \(395 \mathrm{~m}\), find total time of travelling.

1 \(12.2 \mathrm{~s}\)
2 \(15.3 \mathrm{~s}\)
3 \(9 \mathrm{~s}\)
4 \(17.2 \mathrm{~s}\)
Motion in Plane

143746 A river is flowing from west to east with a speed of \(5 \mathrm{~m} / \mathrm{min}\). A man can swim in still water with a velocity \(10 \mathrm{~m} / \mathrm{min}\). In which direction should the man swim so, as to take the shortest possible path to go to the south?

1 \(30^{\circ}\) east of south
2 \(60^{\circ}\) east of south
3 \(60^{\circ}\) west of south
4 \(30^{\circ}\) west of south
Motion in Plane

143742 The speed of a boat is \(5 \mathrm{~km} / \mathrm{h}\) in still water. It crosses a river of width \(1.0 \mathrm{~km}\) along the shortest possible path in \(15 \mathrm{~min}\). The velocity of the river water is (in \(\mathrm{km} / \mathrm{h}\) )

1 5
2 1
3 3
4 4
Motion in Plane

143743 The speed of a swimmer in still water is \(20 \mathrm{~m} / \mathrm{s}\). The speed of river water is \(10 \mathrm{~m} / \mathrm{s}\) 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 \(0^{\circ}\)
2 \(60^{\circ}\) west
3 \(45^{\circ}\) west
4 \(30^{\circ}\) west
Motion in Plane

143744 A ship A is moving Westwards with a speed of \(10 \mathrm{~km} \mathrm{~h}^{-1}\) and a ship \(B 100 \mathrm{~km}\) South of \(A\), is moving Northwards with a speed of \(10 \mathrm{kmh}^{-1}\). The time after which the distance between them becomes shortest is

1 \(0 \mathrm{~h}\)
2 \(5 \mathrm{~h}\)
3 \(10 \sqrt{2} \mathrm{~h}\)
4 \(10 \sqrt{2} \mathrm{~h}\)
Motion in Plane

143745 A metro train starts from rest and in 5 sec achieves \(108 \mathrm{~km} / \mathrm{h}\). After that it moves with constant velocity and comes to rest after travelling \(45 \mathrm{~m}\) with uniform retardation. If total distance travelled is \(395 \mathrm{~m}\), find total time of travelling.

1 \(12.2 \mathrm{~s}\)
2 \(15.3 \mathrm{~s}\)
3 \(9 \mathrm{~s}\)
4 \(17.2 \mathrm{~s}\)
Motion in Plane

143746 A river is flowing from west to east with a speed of \(5 \mathrm{~m} / \mathrm{min}\). A man can swim in still water with a velocity \(10 \mathrm{~m} / \mathrm{min}\). In which direction should the man swim so, as to take the shortest possible path to go to the south?

1 \(30^{\circ}\) east of south
2 \(60^{\circ}\) east of south
3 \(60^{\circ}\) west of south
4 \(30^{\circ}\) west of south