362102
Wind is blowing \(N\)-\(E\) with and steamer is heading due east. In which direction is the flag fluttering?
1 North
2 North-West
3 South
4 South-West
Explanation:
Flag will flutter in the direction of wind w.r.t steamer: \({\overrightarrow v _{WS}} = {\overrightarrow v _W} - {\overrightarrow v _S} = \left( {18\hat i + 18\hat j} \right) - \left( {8\hat i} \right)\) \({\overrightarrow v _{WS}} = 18\hat j\)
PHXI04:MOTION IN A PLANE
362103
An aeroplane flies along a straight line from \(A\) to \(B\) with speed \(v\) and back again with the same speed. If the distance between \(A\) and \(B\) is \(l\) and a steady wind blows perpendicular to \(AB\) with speed \(u\), the total time taken for the round trip is
1 \(\frac{{2\ell }}{v}\)
2 \(\frac{{2\ell }}{{\sqrt {{v^2} + {u^2}} }}\)
3 \(\frac{{2v\ell }}{{v + u}}\)
4 \(\frac{{2\ell }}{{\sqrt {{v^2} - {u^2}} }}\)
Explanation:
Given that \(v\) is the velocity of plane with respect to wind. Consider the motion geometrically. The triangle rule is given in the figure. \({\overrightarrow v _{PW}} - \) Velocity of plane with respect to wind \({\overrightarrow v _W} - \) Velocity of wind w.r.t ground \({\overrightarrow v _P} - \) Velocity of plane w.r.t ground \(v_{pw}^2 = v_p^2 + v_w^2\) \({\overrightarrow v _P} = \sqrt {{v^2} - {u^2}} \) Time for going from \(A\) to \(B\) is \({t_1} = \frac{\ell }{{\sqrt {{v^2} - {u^2}} }}\) The returning motion from \(B\) to \(A\) \({\overrightarrow v _P} = \sqrt {{v^2} - {u^2}} \) (similarly) Time for going from \(B\) to \(A\) is \({t_2} = \frac{\ell }{{\sqrt {{v^2} - {u^2}} }}\) Total time \( = \frac{{2\ell }}{{\sqrt {{v^2} - {u^2}} }}\)
362102
Wind is blowing \(N\)-\(E\) with and steamer is heading due east. In which direction is the flag fluttering?
1 North
2 North-West
3 South
4 South-West
Explanation:
Flag will flutter in the direction of wind w.r.t steamer: \({\overrightarrow v _{WS}} = {\overrightarrow v _W} - {\overrightarrow v _S} = \left( {18\hat i + 18\hat j} \right) - \left( {8\hat i} \right)\) \({\overrightarrow v _{WS}} = 18\hat j\)
PHXI04:MOTION IN A PLANE
362103
An aeroplane flies along a straight line from \(A\) to \(B\) with speed \(v\) and back again with the same speed. If the distance between \(A\) and \(B\) is \(l\) and a steady wind blows perpendicular to \(AB\) with speed \(u\), the total time taken for the round trip is
1 \(\frac{{2\ell }}{v}\)
2 \(\frac{{2\ell }}{{\sqrt {{v^2} + {u^2}} }}\)
3 \(\frac{{2v\ell }}{{v + u}}\)
4 \(\frac{{2\ell }}{{\sqrt {{v^2} - {u^2}} }}\)
Explanation:
Given that \(v\) is the velocity of plane with respect to wind. Consider the motion geometrically. The triangle rule is given in the figure. \({\overrightarrow v _{PW}} - \) Velocity of plane with respect to wind \({\overrightarrow v _W} - \) Velocity of wind w.r.t ground \({\overrightarrow v _P} - \) Velocity of plane w.r.t ground \(v_{pw}^2 = v_p^2 + v_w^2\) \({\overrightarrow v _P} = \sqrt {{v^2} - {u^2}} \) Time for going from \(A\) to \(B\) is \({t_1} = \frac{\ell }{{\sqrt {{v^2} - {u^2}} }}\) The returning motion from \(B\) to \(A\) \({\overrightarrow v _P} = \sqrt {{v^2} - {u^2}} \) (similarly) Time for going from \(B\) to \(A\) is \({t_2} = \frac{\ell }{{\sqrt {{v^2} - {u^2}} }}\) Total time \( = \frac{{2\ell }}{{\sqrt {{v^2} - {u^2}} }}\)
