362085
A boat is sent across a river with a velocity of 8 \(km\)/\(h\). If the resultant velocity of boat is 10 \(km\)/\(h\), then velocity of river is
1 \(10\,km/h\)
2 \(8\,km/h\)
3 \(6\,km/h\)
4 \(4\,km/h\)
Explanation:
Given \(AB = \) velocity of boat \( = 8\,km/h\) \(AC = \) Resultant velocity of boat \( = 10\,km/h\) \(\therefore \,\,\,\,BC = \) Velocity of river \( = \sqrt {A{C^2} - A{B^2}} \) \( = \sqrt {{{(10)}^2} - {{(8)}^2}} = 6\,km/h\)
PHXI04:MOTION IN A PLANE
362086
A swimmer can swim in still water with a speed of \(\sqrt 5 \,m/s.\) While crosses a river his average speed is 3 \(m\)/\(s\). If he cross the river in the shortest possible time, what is the speed of flow of water?
1 \(2\,m/s\)
2 \(4\,m/s\)
3 \(6\,m/s\)
4 \(8\,m/s\)
Explanation:
Let \({v_r}\) is the velocity of river flow. \(3 = \sqrt {{{\left( {\sqrt 5 } \right)}^2} + v_r^2} \, \Rightarrow {v_r} = 2m/s\)
PHXI04:MOTION IN A PLANE
362087
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 \(m\)/\(s\) at an angle with the direction of \(120^\circ \) flow of water. The speed of water is
362088
A river is flowing at the rate of 6 \(km\)/\(hr\) a swimmer swims across the river with a velocity of 9 \(km\)/\(hr\) w.r.t water. The resultant velocity of the man is ( in \(km\)/\(h\))
1 \(\sqrt {117} \)
2 \(\sqrt {340} \)
3 \(\sqrt {17} \)
4 \(3\sqrt {40} \)
Explanation:
Assume that river flow is along \( + x\)-axis and the swimmer swims along \( + y\)-axis w.r.to water Given that \({\overrightarrow v _r} = 6\hat i\) \({\overrightarrow v _{mr}} = 9\hat j\) ( perpendicular to river flow) \({\overrightarrow v _{mr}} = {\overrightarrow v _m} - {\overrightarrow v _r}\) \({\overrightarrow v _m} = \left( {{{\overrightarrow v }_r} + {{\overrightarrow v }_{mr}}} \right)\) \({\overrightarrow v _m} = 6\hat i + 9\hat j\) \({v_m} = \sqrt {117} \,km/h.\)
362085
A boat is sent across a river with a velocity of 8 \(km\)/\(h\). If the resultant velocity of boat is 10 \(km\)/\(h\), then velocity of river is
1 \(10\,km/h\)
2 \(8\,km/h\)
3 \(6\,km/h\)
4 \(4\,km/h\)
Explanation:
Given \(AB = \) velocity of boat \( = 8\,km/h\) \(AC = \) Resultant velocity of boat \( = 10\,km/h\) \(\therefore \,\,\,\,BC = \) Velocity of river \( = \sqrt {A{C^2} - A{B^2}} \) \( = \sqrt {{{(10)}^2} - {{(8)}^2}} = 6\,km/h\)
PHXI04:MOTION IN A PLANE
362086
A swimmer can swim in still water with a speed of \(\sqrt 5 \,m/s.\) While crosses a river his average speed is 3 \(m\)/\(s\). If he cross the river in the shortest possible time, what is the speed of flow of water?
1 \(2\,m/s\)
2 \(4\,m/s\)
3 \(6\,m/s\)
4 \(8\,m/s\)
Explanation:
Let \({v_r}\) is the velocity of river flow. \(3 = \sqrt {{{\left( {\sqrt 5 } \right)}^2} + v_r^2} \, \Rightarrow {v_r} = 2m/s\)
PHXI04:MOTION IN A PLANE
362087
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 \(m\)/\(s\) at an angle with the direction of \(120^\circ \) flow of water. The speed of water is
362088
A river is flowing at the rate of 6 \(km\)/\(hr\) a swimmer swims across the river with a velocity of 9 \(km\)/\(hr\) w.r.t water. The resultant velocity of the man is ( in \(km\)/\(h\))
1 \(\sqrt {117} \)
2 \(\sqrt {340} \)
3 \(\sqrt {17} \)
4 \(3\sqrt {40} \)
Explanation:
Assume that river flow is along \( + x\)-axis and the swimmer swims along \( + y\)-axis w.r.to water Given that \({\overrightarrow v _r} = 6\hat i\) \({\overrightarrow v _{mr}} = 9\hat j\) ( perpendicular to river flow) \({\overrightarrow v _{mr}} = {\overrightarrow v _m} - {\overrightarrow v _r}\) \({\overrightarrow v _m} = \left( {{{\overrightarrow v }_r} + {{\overrightarrow v }_{mr}}} \right)\) \({\overrightarrow v _m} = 6\hat i + 9\hat j\) \({v_m} = \sqrt {117} \,km/h.\)
362085
A boat is sent across a river with a velocity of 8 \(km\)/\(h\). If the resultant velocity of boat is 10 \(km\)/\(h\), then velocity of river is
1 \(10\,km/h\)
2 \(8\,km/h\)
3 \(6\,km/h\)
4 \(4\,km/h\)
Explanation:
Given \(AB = \) velocity of boat \( = 8\,km/h\) \(AC = \) Resultant velocity of boat \( = 10\,km/h\) \(\therefore \,\,\,\,BC = \) Velocity of river \( = \sqrt {A{C^2} - A{B^2}} \) \( = \sqrt {{{(10)}^2} - {{(8)}^2}} = 6\,km/h\)
PHXI04:MOTION IN A PLANE
362086
A swimmer can swim in still water with a speed of \(\sqrt 5 \,m/s.\) While crosses a river his average speed is 3 \(m\)/\(s\). If he cross the river in the shortest possible time, what is the speed of flow of water?
1 \(2\,m/s\)
2 \(4\,m/s\)
3 \(6\,m/s\)
4 \(8\,m/s\)
Explanation:
Let \({v_r}\) is the velocity of river flow. \(3 = \sqrt {{{\left( {\sqrt 5 } \right)}^2} + v_r^2} \, \Rightarrow {v_r} = 2m/s\)
PHXI04:MOTION IN A PLANE
362087
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 \(m\)/\(s\) at an angle with the direction of \(120^\circ \) flow of water. The speed of water is
362088
A river is flowing at the rate of 6 \(km\)/\(hr\) a swimmer swims across the river with a velocity of 9 \(km\)/\(hr\) w.r.t water. The resultant velocity of the man is ( in \(km\)/\(h\))
1 \(\sqrt {117} \)
2 \(\sqrt {340} \)
3 \(\sqrt {17} \)
4 \(3\sqrt {40} \)
Explanation:
Assume that river flow is along \( + x\)-axis and the swimmer swims along \( + y\)-axis w.r.to water Given that \({\overrightarrow v _r} = 6\hat i\) \({\overrightarrow v _{mr}} = 9\hat j\) ( perpendicular to river flow) \({\overrightarrow v _{mr}} = {\overrightarrow v _m} - {\overrightarrow v _r}\) \({\overrightarrow v _m} = \left( {{{\overrightarrow v }_r} + {{\overrightarrow v }_{mr}}} \right)\) \({\overrightarrow v _m} = 6\hat i + 9\hat j\) \({v_m} = \sqrt {117} \,km/h.\)
362085
A boat is sent across a river with a velocity of 8 \(km\)/\(h\). If the resultant velocity of boat is 10 \(km\)/\(h\), then velocity of river is
1 \(10\,km/h\)
2 \(8\,km/h\)
3 \(6\,km/h\)
4 \(4\,km/h\)
Explanation:
Given \(AB = \) velocity of boat \( = 8\,km/h\) \(AC = \) Resultant velocity of boat \( = 10\,km/h\) \(\therefore \,\,\,\,BC = \) Velocity of river \( = \sqrt {A{C^2} - A{B^2}} \) \( = \sqrt {{{(10)}^2} - {{(8)}^2}} = 6\,km/h\)
PHXI04:MOTION IN A PLANE
362086
A swimmer can swim in still water with a speed of \(\sqrt 5 \,m/s.\) While crosses a river his average speed is 3 \(m\)/\(s\). If he cross the river in the shortest possible time, what is the speed of flow of water?
1 \(2\,m/s\)
2 \(4\,m/s\)
3 \(6\,m/s\)
4 \(8\,m/s\)
Explanation:
Let \({v_r}\) is the velocity of river flow. \(3 = \sqrt {{{\left( {\sqrt 5 } \right)}^2} + v_r^2} \, \Rightarrow {v_r} = 2m/s\)
PHXI04:MOTION IN A PLANE
362087
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 \(m\)/\(s\) at an angle with the direction of \(120^\circ \) flow of water. The speed of water is
362088
A river is flowing at the rate of 6 \(km\)/\(hr\) a swimmer swims across the river with a velocity of 9 \(km\)/\(hr\) w.r.t water. The resultant velocity of the man is ( in \(km\)/\(h\))
1 \(\sqrt {117} \)
2 \(\sqrt {340} \)
3 \(\sqrt {17} \)
4 \(3\sqrt {40} \)
Explanation:
Assume that river flow is along \( + x\)-axis and the swimmer swims along \( + y\)-axis w.r.to water Given that \({\overrightarrow v _r} = 6\hat i\) \({\overrightarrow v _{mr}} = 9\hat j\) ( perpendicular to river flow) \({\overrightarrow v _{mr}} = {\overrightarrow v _m} - {\overrightarrow v _r}\) \({\overrightarrow v _m} = \left( {{{\overrightarrow v }_r} + {{\overrightarrow v }_{mr}}} \right)\) \({\overrightarrow v _m} = 6\hat i + 9\hat j\) \({v_m} = \sqrt {117} \,km/h.\)
