Relative Motion in Two Dimensions
PHXI04:MOTION IN A PLANE

362076 Rain is falling vertically with a speed of \(35\,m\,s{}^{ - 1}.\) Wind starts blowing after sometime with a speed of \(12\,m\,{s^{ - 1}}\) in east to west direction. At what angle with the vertical should a boy waiting at a bus stop hold his umbrella to protect himself from rain?

1 \({\sin ^{ - 1}}\left( {\frac{{12}}{{35}}} \right)\)
2 \({\cos ^{ - 1}}\left( {\frac{{12}}{{35}}} \right)\)
3 \({\tan ^{ - 1}}\left( {\frac{{12}}{{35}}} \right)\)
4 \({\cot ^{ - 1}}\left( {\frac{{12}}{{35}}} \right)\)
PHXI04:MOTION IN A PLANE

362077 Rain is falling vertically with a speed of 30 \(m\)/\(s\). A woman rides a bicycle with a speed of 10 \(m\)/\(s\) on a road. What is the direction in which she should hold her umbrella?

1 \({\tan ^{ - 1}}3\) with vertical
2 \({\tan ^{ - 1}}\frac{1}{3}\) with vertical
3 \({\tan ^{ - 1}}\frac{3}{{\sqrt {10} }}\) with horizontal
4 \({\rm{Vertical}}\)
PHXI04:MOTION IN A PLANE

362078 Police is chasing the thief \(50\;m\) ahead. In \(10\;I,\) distance between them reduces by \(6\;m.\) What is distance between them in \(25 s\) ?

1 \(10\;m\)
2 \(25\;m\)
3 \(35\;m\)
4 \(20\;m\)
PHXI04:MOTION IN A PLANE

362079 Rain water is falling vertically downwards with velocity \(v\), when the velocity of wind is zero, water is collected at a rate \(R\). When the wind starts blowing horizontally at a speed \(u\), the rate of collection of water in the same vessel is:

1 \(\sqrt{u^{2}+v^{2} R}\)
2 \(\dfrac{v}{u} R\)
3 \(\dfrac{u R}{v}\)
4 \(R\)
PHXI04:MOTION IN A PLANE

362080 A man wants to reach point \(B\) on the opposite bank of a river flowing at a speed as shown in figure. What minimum speed relative to water should the man have so that he can reach point \(B\)?
supporting img

1 \(u\sqrt 2 \)
2 \(u/\sqrt 2 \)
3 \(2u\)
4 \(u/2\)
PHXI04:MOTION IN A PLANE

362076 Rain is falling vertically with a speed of \(35\,m\,s{}^{ - 1}.\) Wind starts blowing after sometime with a speed of \(12\,m\,{s^{ - 1}}\) in east to west direction. At what angle with the vertical should a boy waiting at a bus stop hold his umbrella to protect himself from rain?

1 \({\sin ^{ - 1}}\left( {\frac{{12}}{{35}}} \right)\)
2 \({\cos ^{ - 1}}\left( {\frac{{12}}{{35}}} \right)\)
3 \({\tan ^{ - 1}}\left( {\frac{{12}}{{35}}} \right)\)
4 \({\cot ^{ - 1}}\left( {\frac{{12}}{{35}}} \right)\)
PHXI04:MOTION IN A PLANE

362077 Rain is falling vertically with a speed of 30 \(m\)/\(s\). A woman rides a bicycle with a speed of 10 \(m\)/\(s\) on a road. What is the direction in which she should hold her umbrella?

1 \({\tan ^{ - 1}}3\) with vertical
2 \({\tan ^{ - 1}}\frac{1}{3}\) with vertical
3 \({\tan ^{ - 1}}\frac{3}{{\sqrt {10} }}\) with horizontal
4 \({\rm{Vertical}}\)
PHXI04:MOTION IN A PLANE

362078 Police is chasing the thief \(50\;m\) ahead. In \(10\;I,\) distance between them reduces by \(6\;m.\) What is distance between them in \(25 s\) ?

1 \(10\;m\)
2 \(25\;m\)
3 \(35\;m\)
4 \(20\;m\)
PHXI04:MOTION IN A PLANE

362079 Rain water is falling vertically downwards with velocity \(v\), when the velocity of wind is zero, water is collected at a rate \(R\). When the wind starts blowing horizontally at a speed \(u\), the rate of collection of water in the same vessel is:

1 \(\sqrt{u^{2}+v^{2} R}\)
2 \(\dfrac{v}{u} R\)
3 \(\dfrac{u R}{v}\)
4 \(R\)
PHXI04:MOTION IN A PLANE

362080 A man wants to reach point \(B\) on the opposite bank of a river flowing at a speed as shown in figure. What minimum speed relative to water should the man have so that he can reach point \(B\)?
supporting img

1 \(u\sqrt 2 \)
2 \(u/\sqrt 2 \)
3 \(2u\)
4 \(u/2\)
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PHXI04:MOTION IN A PLANE

362076 Rain is falling vertically with a speed of \(35\,m\,s{}^{ - 1}.\) Wind starts blowing after sometime with a speed of \(12\,m\,{s^{ - 1}}\) in east to west direction. At what angle with the vertical should a boy waiting at a bus stop hold his umbrella to protect himself from rain?

1 \({\sin ^{ - 1}}\left( {\frac{{12}}{{35}}} \right)\)
2 \({\cos ^{ - 1}}\left( {\frac{{12}}{{35}}} \right)\)
3 \({\tan ^{ - 1}}\left( {\frac{{12}}{{35}}} \right)\)
4 \({\cot ^{ - 1}}\left( {\frac{{12}}{{35}}} \right)\)
PHXI04:MOTION IN A PLANE

362077 Rain is falling vertically with a speed of 30 \(m\)/\(s\). A woman rides a bicycle with a speed of 10 \(m\)/\(s\) on a road. What is the direction in which she should hold her umbrella?

1 \({\tan ^{ - 1}}3\) with vertical
2 \({\tan ^{ - 1}}\frac{1}{3}\) with vertical
3 \({\tan ^{ - 1}}\frac{3}{{\sqrt {10} }}\) with horizontal
4 \({\rm{Vertical}}\)
PHXI04:MOTION IN A PLANE

362078 Police is chasing the thief \(50\;m\) ahead. In \(10\;I,\) distance between them reduces by \(6\;m.\) What is distance between them in \(25 s\) ?

1 \(10\;m\)
2 \(25\;m\)
3 \(35\;m\)
4 \(20\;m\)
PHXI04:MOTION IN A PLANE

362079 Rain water is falling vertically downwards with velocity \(v\), when the velocity of wind is zero, water is collected at a rate \(R\). When the wind starts blowing horizontally at a speed \(u\), the rate of collection of water in the same vessel is:

1 \(\sqrt{u^{2}+v^{2} R}\)
2 \(\dfrac{v}{u} R\)
3 \(\dfrac{u R}{v}\)
4 \(R\)
PHXI04:MOTION IN A PLANE

362080 A man wants to reach point \(B\) on the opposite bank of a river flowing at a speed as shown in figure. What minimum speed relative to water should the man have so that he can reach point \(B\)?
supporting img

1 \(u\sqrt 2 \)
2 \(u/\sqrt 2 \)
3 \(2u\)
4 \(u/2\)
PHXI04:MOTION IN A PLANE

362076 Rain is falling vertically with a speed of \(35\,m\,s{}^{ - 1}.\) Wind starts blowing after sometime with a speed of \(12\,m\,{s^{ - 1}}\) in east to west direction. At what angle with the vertical should a boy waiting at a bus stop hold his umbrella to protect himself from rain?

1 \({\sin ^{ - 1}}\left( {\frac{{12}}{{35}}} \right)\)
2 \({\cos ^{ - 1}}\left( {\frac{{12}}{{35}}} \right)\)
3 \({\tan ^{ - 1}}\left( {\frac{{12}}{{35}}} \right)\)
4 \({\cot ^{ - 1}}\left( {\frac{{12}}{{35}}} \right)\)
PHXI04:MOTION IN A PLANE

362077 Rain is falling vertically with a speed of 30 \(m\)/\(s\). A woman rides a bicycle with a speed of 10 \(m\)/\(s\) on a road. What is the direction in which she should hold her umbrella?

1 \({\tan ^{ - 1}}3\) with vertical
2 \({\tan ^{ - 1}}\frac{1}{3}\) with vertical
3 \({\tan ^{ - 1}}\frac{3}{{\sqrt {10} }}\) with horizontal
4 \({\rm{Vertical}}\)
PHXI04:MOTION IN A PLANE

362078 Police is chasing the thief \(50\;m\) ahead. In \(10\;I,\) distance between them reduces by \(6\;m.\) What is distance between them in \(25 s\) ?

1 \(10\;m\)
2 \(25\;m\)
3 \(35\;m\)
4 \(20\;m\)
PHXI04:MOTION IN A PLANE

362079 Rain water is falling vertically downwards with velocity \(v\), when the velocity of wind is zero, water is collected at a rate \(R\). When the wind starts blowing horizontally at a speed \(u\), the rate of collection of water in the same vessel is:

1 \(\sqrt{u^{2}+v^{2} R}\)
2 \(\dfrac{v}{u} R\)
3 \(\dfrac{u R}{v}\)
4 \(R\)
PHXI04:MOTION IN A PLANE

362080 A man wants to reach point \(B\) on the opposite bank of a river flowing at a speed as shown in figure. What minimum speed relative to water should the man have so that he can reach point \(B\)?
supporting img

1 \(u\sqrt 2 \)
2 \(u/\sqrt 2 \)
3 \(2u\)
4 \(u/2\)
PHXI04:MOTION IN A PLANE

362076 Rain is falling vertically with a speed of \(35\,m\,s{}^{ - 1}.\) Wind starts blowing after sometime with a speed of \(12\,m\,{s^{ - 1}}\) in east to west direction. At what angle with the vertical should a boy waiting at a bus stop hold his umbrella to protect himself from rain?

1 \({\sin ^{ - 1}}\left( {\frac{{12}}{{35}}} \right)\)
2 \({\cos ^{ - 1}}\left( {\frac{{12}}{{35}}} \right)\)
3 \({\tan ^{ - 1}}\left( {\frac{{12}}{{35}}} \right)\)
4 \({\cot ^{ - 1}}\left( {\frac{{12}}{{35}}} \right)\)
PHXI04:MOTION IN A PLANE

362077 Rain is falling vertically with a speed of 30 \(m\)/\(s\). A woman rides a bicycle with a speed of 10 \(m\)/\(s\) on a road. What is the direction in which she should hold her umbrella?

1 \({\tan ^{ - 1}}3\) with vertical
2 \({\tan ^{ - 1}}\frac{1}{3}\) with vertical
3 \({\tan ^{ - 1}}\frac{3}{{\sqrt {10} }}\) with horizontal
4 \({\rm{Vertical}}\)
PHXI04:MOTION IN A PLANE

362078 Police is chasing the thief \(50\;m\) ahead. In \(10\;I,\) distance between them reduces by \(6\;m.\) What is distance between them in \(25 s\) ?

1 \(10\;m\)
2 \(25\;m\)
3 \(35\;m\)
4 \(20\;m\)
PHXI04:MOTION IN A PLANE

362079 Rain water is falling vertically downwards with velocity \(v\), when the velocity of wind is zero, water is collected at a rate \(R\). When the wind starts blowing horizontally at a speed \(u\), the rate of collection of water in the same vessel is:

1 \(\sqrt{u^{2}+v^{2} R}\)
2 \(\dfrac{v}{u} R\)
3 \(\dfrac{u R}{v}\)
4 \(R\)
PHXI04:MOTION IN A PLANE

362080 A man wants to reach point \(B\) on the opposite bank of a river flowing at a speed as shown in figure. What minimum speed relative to water should the man have so that he can reach point \(B\)?
supporting img

1 \(u\sqrt 2 \)
2 \(u/\sqrt 2 \)
3 \(2u\)
4 \(u/2\)