- 1(current)
Q. No.Rain is falling vertically downward with a speed of \(35~\text{m/s}.\) The wind starts blowing after some time with a speed of \(12~\text{m/s}\) in the east to the west direction. The direction in which a boy standing at the place should hold his umbrella is:
| 1. | \(\text{tan}^{-1}\Big(\frac{12}{37}\Big)\) with respect to rain |
| 2. | \(\text{tan}^{-1}\Big(\frac{12}{37}\Big)\) with respect to wind |
| 3. | \(\text{tan}^{-1}\Big(\frac{12}{35}\Big)\) with respect to rain |
| 4. | \(\text{tan}^{-1}\Big(\frac{12}{35}\Big)\) with respect to wind |
The speed of a swimmer in still water is \(20~\text{m/s}.\) The speed of river water is \(10~\text{m/s}\) 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 with respect to the north is given by:
| 1. | \(45^{\circ}\) west of north | 2. | \(30^{\circ}\) west of north |
| 3. | \(0^{\circ}\) west of north | 4. | \(60^{\circ}\) west of north |
Two bullets are fired horizontally and simultaneously towards each other from the rooftops of two buildings (building being \(100~\text{m}\) apart and being of the same height of \(200~\text{m}\)) with the same velocity of \(25~\text{m/s}.\) When and where will the two bullets collide?
\((g = 10~\text{m/s}^2)\)
| 1. | After \(2~\text{s}\) at a height of \(180~\text{m}\) |
| 2. | After \(2~\text{s}\) at a height of \(20~\text{m}\) |
| 3. | After \(4~\text{s}\) at a height of \(120~\text{m}\) |
| 4. | They will not collide. |
Preeti reached the metro station and found that the escalator was not working. She walked up the stationary escalator in time \(t_1\). On other days, if she remains stationary on the moving escalator, then the escalator takes her up in time \(t_2\). The time taken by her to walk up on the moving escalator will be:
1. \(\dfrac{t_1-t_2}{2}\)
2. \(\dfrac{t_1t_2}{t_2-t_1}\)
3. \(\dfrac{t_1t_2}{t_2+t_1}\)
4. \(t_1-t_2\)
- 1(current)
Q. No.
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