362068
A man is walking on a level road at a speed of \(3.0\,km{\rm{/}}h\). Rain drops fall vertically with a speed of \(4.0\,km{\rm{/}}h\). Find the velocity of the raindrops with respect to the man.
1 \(5.0\;\,km{\rm{/}}h\)
2 \(2.0\;\,km{\rm{/}}h\)
3 \(7.0\;\,km{\rm{/}}h\)
4 \(9.0\;\,km{\rm{/}}h\)
Explanation:
We have to find the velocity of raindrops with respect to the man. The velocity of the rain as well as the velocity of the man are given with respect to the street. We have \(\vec{v}_{\text {rain,man }}=\vec{v}_{\text {rain,street }}-\vec{v}_{\text {rain,street }}\). Figure shows the velocities It is clear from the figure that \({\vec v_{rain,man{\rm{ }}}}{\rm{ }} = \sqrt {{{(4 \cdot 0\;km{\rm{/}}h)}^2} + {{(3 \cdot 0\;km{\rm{/}}h)}^2}} \) \( = 5.0\;km{\rm{/}}h.\)
PHXI04:MOTION IN A PLANE
362069
A man starts from rest with an acceleration \(1\;m{s^{ - 2}}\) at \(t=0\). At \(t = 3\sqrt 3 \;s\), it appears to him that rain falls with the velocity \(3\;m{s^{ - 1}}\) vertically downwards. The velocity of actual rain fall is
1 \(3\sqrt 3 \;m{s^{ - 1}}\)
2 \(3\;m{s^{ - 1}}\)
3 \(6\;m{s^{ - 1}}\)
4 \(6\sqrt 3 \;m{s^{ - 1}}\)
Explanation:
Let the velocity of rain fall is \(v_{r}\). The velocity of man at \(t=3 \sqrt{3} \mathrm{~s}\) is \(v_{m}=u+a t=0+3 \sqrt{3} \times 1\) \( = 3\sqrt 3 \;m{s^{ - 1}}\) According to the problem, \({v_{rm}} = 3\;m{s^{ - 1}}\)vertically downward. \(\because v_{r m}=v_{r}-v_{m}\) or \(v_{r}=v_{r m}+v_{m}\) \(\Rightarrow v_{r}=3 \hat{j}+3 \sqrt{3} \hat{i}\) \(\therefore v_{r}=\sqrt{(3 \sqrt{3})^{2}+3^{2}}\) \( = \sqrt {27 + 9} = \sqrt {36} = 6\;m{s^{ - 1}}\)
PHXI04:MOTION IN A PLANE
362070
Wind is blowing in the north direction at speed of 4\(m\)/\(s\) which causes the rain to fall at some angle with the vertical. With what velocity should a cyclist drive so that the rain appears vertical to him?
1 \(4\,m/s\) north
2 \(4\,m/s\) south
3 \(2\,m/s\) south
4 \(2\,m/s\) west
Explanation:
Horizontal component of rain’s velocity will be equal to velocity of wind which is 4 \(m\)/\(s\) in north direction. If cyclist goes towards north with velocity 4 \(m\)/\(s\), then w.r.t ‘him’ rain’s horizontal component of velocity will be zero, and he will see only vertical component.
PHXI04:MOTION IN A PLANE
362071
Wind is blowing in the north direction at speed of \(2\,m/s\) which causes the rain to fall at some angle with the vertical. With what velocity should a cyclist drive so that the rain appears vertical to him?
1 \(2\,m/s\) south
2 \(2\,m/s\) north
3 \(4\,m/s\) west
4 \(4\,m/s\) south
Explanation:
Horizontal component of rain’s velocity will be equal to velocity of wind which is 2 \(m\)/\(s\) in north direction. If cyclist goes towards north with velocity 2 \(m\)/\(s\), then w.r.t ‘him’ rain’s horizontal component of velocity will be zero, and he will see only vertical component.
NEET Test Series from KOTA - 10 Papers In MS WORD
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PHXI04:MOTION IN A PLANE
362068
A man is walking on a level road at a speed of \(3.0\,km{\rm{/}}h\). Rain drops fall vertically with a speed of \(4.0\,km{\rm{/}}h\). Find the velocity of the raindrops with respect to the man.
1 \(5.0\;\,km{\rm{/}}h\)
2 \(2.0\;\,km{\rm{/}}h\)
3 \(7.0\;\,km{\rm{/}}h\)
4 \(9.0\;\,km{\rm{/}}h\)
Explanation:
We have to find the velocity of raindrops with respect to the man. The velocity of the rain as well as the velocity of the man are given with respect to the street. We have \(\vec{v}_{\text {rain,man }}=\vec{v}_{\text {rain,street }}-\vec{v}_{\text {rain,street }}\). Figure shows the velocities It is clear from the figure that \({\vec v_{rain,man{\rm{ }}}}{\rm{ }} = \sqrt {{{(4 \cdot 0\;km{\rm{/}}h)}^2} + {{(3 \cdot 0\;km{\rm{/}}h)}^2}} \) \( = 5.0\;km{\rm{/}}h.\)
PHXI04:MOTION IN A PLANE
362069
A man starts from rest with an acceleration \(1\;m{s^{ - 2}}\) at \(t=0\). At \(t = 3\sqrt 3 \;s\), it appears to him that rain falls with the velocity \(3\;m{s^{ - 1}}\) vertically downwards. The velocity of actual rain fall is
1 \(3\sqrt 3 \;m{s^{ - 1}}\)
2 \(3\;m{s^{ - 1}}\)
3 \(6\;m{s^{ - 1}}\)
4 \(6\sqrt 3 \;m{s^{ - 1}}\)
Explanation:
Let the velocity of rain fall is \(v_{r}\). The velocity of man at \(t=3 \sqrt{3} \mathrm{~s}\) is \(v_{m}=u+a t=0+3 \sqrt{3} \times 1\) \( = 3\sqrt 3 \;m{s^{ - 1}}\) According to the problem, \({v_{rm}} = 3\;m{s^{ - 1}}\)vertically downward. \(\because v_{r m}=v_{r}-v_{m}\) or \(v_{r}=v_{r m}+v_{m}\) \(\Rightarrow v_{r}=3 \hat{j}+3 \sqrt{3} \hat{i}\) \(\therefore v_{r}=\sqrt{(3 \sqrt{3})^{2}+3^{2}}\) \( = \sqrt {27 + 9} = \sqrt {36} = 6\;m{s^{ - 1}}\)
PHXI04:MOTION IN A PLANE
362070
Wind is blowing in the north direction at speed of 4\(m\)/\(s\) which causes the rain to fall at some angle with the vertical. With what velocity should a cyclist drive so that the rain appears vertical to him?
1 \(4\,m/s\) north
2 \(4\,m/s\) south
3 \(2\,m/s\) south
4 \(2\,m/s\) west
Explanation:
Horizontal component of rain’s velocity will be equal to velocity of wind which is 4 \(m\)/\(s\) in north direction. If cyclist goes towards north with velocity 4 \(m\)/\(s\), then w.r.t ‘him’ rain’s horizontal component of velocity will be zero, and he will see only vertical component.
PHXI04:MOTION IN A PLANE
362071
Wind is blowing in the north direction at speed of \(2\,m/s\) which causes the rain to fall at some angle with the vertical. With what velocity should a cyclist drive so that the rain appears vertical to him?
1 \(2\,m/s\) south
2 \(2\,m/s\) north
3 \(4\,m/s\) west
4 \(4\,m/s\) south
Explanation:
Horizontal component of rain’s velocity will be equal to velocity of wind which is 2 \(m\)/\(s\) in north direction. If cyclist goes towards north with velocity 2 \(m\)/\(s\), then w.r.t ‘him’ rain’s horizontal component of velocity will be zero, and he will see only vertical component.
362068
A man is walking on a level road at a speed of \(3.0\,km{\rm{/}}h\). Rain drops fall vertically with a speed of \(4.0\,km{\rm{/}}h\). Find the velocity of the raindrops with respect to the man.
1 \(5.0\;\,km{\rm{/}}h\)
2 \(2.0\;\,km{\rm{/}}h\)
3 \(7.0\;\,km{\rm{/}}h\)
4 \(9.0\;\,km{\rm{/}}h\)
Explanation:
We have to find the velocity of raindrops with respect to the man. The velocity of the rain as well as the velocity of the man are given with respect to the street. We have \(\vec{v}_{\text {rain,man }}=\vec{v}_{\text {rain,street }}-\vec{v}_{\text {rain,street }}\). Figure shows the velocities It is clear from the figure that \({\vec v_{rain,man{\rm{ }}}}{\rm{ }} = \sqrt {{{(4 \cdot 0\;km{\rm{/}}h)}^2} + {{(3 \cdot 0\;km{\rm{/}}h)}^2}} \) \( = 5.0\;km{\rm{/}}h.\)
PHXI04:MOTION IN A PLANE
362069
A man starts from rest with an acceleration \(1\;m{s^{ - 2}}\) at \(t=0\). At \(t = 3\sqrt 3 \;s\), it appears to him that rain falls with the velocity \(3\;m{s^{ - 1}}\) vertically downwards. The velocity of actual rain fall is
1 \(3\sqrt 3 \;m{s^{ - 1}}\)
2 \(3\;m{s^{ - 1}}\)
3 \(6\;m{s^{ - 1}}\)
4 \(6\sqrt 3 \;m{s^{ - 1}}\)
Explanation:
Let the velocity of rain fall is \(v_{r}\). The velocity of man at \(t=3 \sqrt{3} \mathrm{~s}\) is \(v_{m}=u+a t=0+3 \sqrt{3} \times 1\) \( = 3\sqrt 3 \;m{s^{ - 1}}\) According to the problem, \({v_{rm}} = 3\;m{s^{ - 1}}\)vertically downward. \(\because v_{r m}=v_{r}-v_{m}\) or \(v_{r}=v_{r m}+v_{m}\) \(\Rightarrow v_{r}=3 \hat{j}+3 \sqrt{3} \hat{i}\) \(\therefore v_{r}=\sqrt{(3 \sqrt{3})^{2}+3^{2}}\) \( = \sqrt {27 + 9} = \sqrt {36} = 6\;m{s^{ - 1}}\)
PHXI04:MOTION IN A PLANE
362070
Wind is blowing in the north direction at speed of 4\(m\)/\(s\) which causes the rain to fall at some angle with the vertical. With what velocity should a cyclist drive so that the rain appears vertical to him?
1 \(4\,m/s\) north
2 \(4\,m/s\) south
3 \(2\,m/s\) south
4 \(2\,m/s\) west
Explanation:
Horizontal component of rain’s velocity will be equal to velocity of wind which is 4 \(m\)/\(s\) in north direction. If cyclist goes towards north with velocity 4 \(m\)/\(s\), then w.r.t ‘him’ rain’s horizontal component of velocity will be zero, and he will see only vertical component.
PHXI04:MOTION IN A PLANE
362071
Wind is blowing in the north direction at speed of \(2\,m/s\) which causes the rain to fall at some angle with the vertical. With what velocity should a cyclist drive so that the rain appears vertical to him?
1 \(2\,m/s\) south
2 \(2\,m/s\) north
3 \(4\,m/s\) west
4 \(4\,m/s\) south
Explanation:
Horizontal component of rain’s velocity will be equal to velocity of wind which is 2 \(m\)/\(s\) in north direction. If cyclist goes towards north with velocity 2 \(m\)/\(s\), then w.r.t ‘him’ rain’s horizontal component of velocity will be zero, and he will see only vertical component.
362068
A man is walking on a level road at a speed of \(3.0\,km{\rm{/}}h\). Rain drops fall vertically with a speed of \(4.0\,km{\rm{/}}h\). Find the velocity of the raindrops with respect to the man.
1 \(5.0\;\,km{\rm{/}}h\)
2 \(2.0\;\,km{\rm{/}}h\)
3 \(7.0\;\,km{\rm{/}}h\)
4 \(9.0\;\,km{\rm{/}}h\)
Explanation:
We have to find the velocity of raindrops with respect to the man. The velocity of the rain as well as the velocity of the man are given with respect to the street. We have \(\vec{v}_{\text {rain,man }}=\vec{v}_{\text {rain,street }}-\vec{v}_{\text {rain,street }}\). Figure shows the velocities It is clear from the figure that \({\vec v_{rain,man{\rm{ }}}}{\rm{ }} = \sqrt {{{(4 \cdot 0\;km{\rm{/}}h)}^2} + {{(3 \cdot 0\;km{\rm{/}}h)}^2}} \) \( = 5.0\;km{\rm{/}}h.\)
PHXI04:MOTION IN A PLANE
362069
A man starts from rest with an acceleration \(1\;m{s^{ - 2}}\) at \(t=0\). At \(t = 3\sqrt 3 \;s\), it appears to him that rain falls with the velocity \(3\;m{s^{ - 1}}\) vertically downwards. The velocity of actual rain fall is
1 \(3\sqrt 3 \;m{s^{ - 1}}\)
2 \(3\;m{s^{ - 1}}\)
3 \(6\;m{s^{ - 1}}\)
4 \(6\sqrt 3 \;m{s^{ - 1}}\)
Explanation:
Let the velocity of rain fall is \(v_{r}\). The velocity of man at \(t=3 \sqrt{3} \mathrm{~s}\) is \(v_{m}=u+a t=0+3 \sqrt{3} \times 1\) \( = 3\sqrt 3 \;m{s^{ - 1}}\) According to the problem, \({v_{rm}} = 3\;m{s^{ - 1}}\)vertically downward. \(\because v_{r m}=v_{r}-v_{m}\) or \(v_{r}=v_{r m}+v_{m}\) \(\Rightarrow v_{r}=3 \hat{j}+3 \sqrt{3} \hat{i}\) \(\therefore v_{r}=\sqrt{(3 \sqrt{3})^{2}+3^{2}}\) \( = \sqrt {27 + 9} = \sqrt {36} = 6\;m{s^{ - 1}}\)
PHXI04:MOTION IN A PLANE
362070
Wind is blowing in the north direction at speed of 4\(m\)/\(s\) which causes the rain to fall at some angle with the vertical. With what velocity should a cyclist drive so that the rain appears vertical to him?
1 \(4\,m/s\) north
2 \(4\,m/s\) south
3 \(2\,m/s\) south
4 \(2\,m/s\) west
Explanation:
Horizontal component of rain’s velocity will be equal to velocity of wind which is 4 \(m\)/\(s\) in north direction. If cyclist goes towards north with velocity 4 \(m\)/\(s\), then w.r.t ‘him’ rain’s horizontal component of velocity will be zero, and he will see only vertical component.
PHXI04:MOTION IN A PLANE
362071
Wind is blowing in the north direction at speed of \(2\,m/s\) which causes the rain to fall at some angle with the vertical. With what velocity should a cyclist drive so that the rain appears vertical to him?
1 \(2\,m/s\) south
2 \(2\,m/s\) north
3 \(4\,m/s\) west
4 \(4\,m/s\) south
Explanation:
Horizontal component of rain’s velocity will be equal to velocity of wind which is 2 \(m\)/\(s\) in north direction. If cyclist goes towards north with velocity 2 \(m\)/\(s\), then w.r.t ‘him’ rain’s horizontal component of velocity will be zero, and he will see only vertical component.
