Q. No.Rain is falling vertically with a speed of 35 . Winds starts blowing after sometime with a speed of 12 in east to west direction. At what angle should a boy waiting at a bus stop hold his umbrella?
1. with the vertical
2. with the vertical
3. with the vertical
4. with the horizontal
A motorboat is racing towards the north at 25 km/h and the water current in that region is 10 km/h in the direction of 60° east of the south. The resultant velocity of the boat is:
1. 12 km/h at east of west
2. 22 km/h at north of east
3. 22 km/h at east of north
4. 20 km/h at north of wast
The position of a particle is given by; \(\vec{r}=(3.0t\hat{i}-2.0t^{2}\hat{j}+4.0\hat{k})\) m
where \(t\) is in seconds and the coefficients have the proper units for \(r\) to be in meters. The magnitude and direction of \(\vec{v}(t)\) at \(t=1.0\) s are:
| 1. | \(4\) m/s \(53^\circ\) with x-axis |
| 2. | \(4\) m/s \(37^\circ\) with x-axis |
| 3. | \(5\) m/s \(53^\circ\) with y-axis |
| 4. | \(5\) m/s \(53^\circ\) with x-axis |
A particle starts from the origin at t = 0 with a velocity of 5.0î m/s and moves in the x-y plane under the action of a force that produces a constant acceleration of (3.0î +2.0 ĵ ) . What is the speed of the particle at the instant its x-coordinate is 84 m?
| 1. | 36 m/s | 2. | 26 m/s |
| 3. | 1 m/s | 4. | 0 m/s |
Rain is falling vertically with a speed of \(35\) m/s. A woman rides a bicycle with a speed of \(12\) m/s in the east-to-west direction. What is the direction in which she should hold her umbrella?
| 1. | in the vertical direction only. |
| 2. | \(19^\circ\) with vertical towards east. |
| 3. | \(19^\circ\) with vertical towards the west. |
| 4. | \(19^\circ\) with vertical towards the south. |
Galileo, in his book Two new sciences, stated that for elevations that exceed or fall short of \(45^\circ\) by equal amounts, the ranges:
| 1. | are equal to each other. |
| 2. | are not equal to each other. |
| 3. | are sometimes equal and sometimes not equal to each other. |
| 4. | depends on the difference between the angles. |
A hiker stands on the edge of a cliff \(490~\mathrm{m}\) above the ground and throws a stone horizontally with an initial speed of \(15\) m/s. Neglecting air resistance, the time taken by the stone to reach the ground and the speed with which it hits the ground are, respectively: (Take \(g=9.8~\mathrm{m/s^2}\))
| 1. | \(10\) s and \(99\) m/s |
| 2. | \(10\) s and \(15\) m/s |
| 3. | \(5\) s and \(99\) m/s |
| 4. | \(5\) s and \(15\) m/s |
A cricket ball is thrown at a speed of \(28\) m/s in a direction \(30^\circ\) above the horizontal. The time taken by the ball to return to the same level is:
1. \(2.5\) s
2. \(2.9\) s
3. \(3.5\) s
4. \(3\) s
An insect trapped in a circular groove of radius \(12\) cm moves along the groove steadily and completes \(7\) revolutions in \(100\) s. What is the angular speed of the motion?
1.\(0.62\) rad/s
2.\(0.06\) rad/s
3. \(4.40\) rad/s
4. \(0.44\) rad/s
An insect trapped in a circular groove of radius \(12\) cm moves along the groove steadily and completes \(7\) revolutions in \(100\) s. Is the acceleration vector a constant vector? What is its magnitude?
1. \(\mathrm{yes},\) \(2.3~\mathrm{cm/s^2}\)
2. \(\mathrm{no},\) \(5.3~\mathrm{cm/s^2}\)
3. \(\mathrm{yes},\) \(5.3~\mathrm{cm/s^2}\)
4. \(\mathrm{no},\) \(2.3~\mathrm{cm/s^2}\)
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