A man can row a boat with a speed of \(10~\text{kmph}\) in still water. The river flows at \(6~\text{kmph}.\) If he crosses the river from one bank to the other along the shortest possible path, the time taken to cross the river of width \(1~\text{km}\) is:
1. \(\frac{1}{8}~\text{hr}\)
2. \(\frac{1}{4}~\text{hr}\)
3. \(\frac{1}{2}~\text{hr}\)
4. \(1~\text{hr}\)
A bus is going to the North at a speed of \(30\) kmph. It makes a \(90^{\circ}\) left turn without changing the speed. The change in the velocity of the bus is:
1. | \(30~\text{kmph}\) towards \(\mathrm{W}\) |
2. | \(30~\text{kmph}\) towards \(\mathrm{S\text-W}\) |
3. | \(42.4~\text{kmph}\) towards \(\mathrm{S\text-W}\) |
4. | \(42.4~\text{kmph}\) towards \(\mathrm{N\text-W}\) |
Two bullets are fired simultaneously horizontally and at different speeds from the same place. Which bullet will hit the ground first? (Air resistance is neglected)
1. | The faster one |
2. | The slower one |
3. | Depends on masses |
4. | Both will reach simultaneously |
A pilot is supposed to fly east from A to B and back again A due west. If the wind is blowing due south, find time for the round trip, if AB = l. The velocity of the plane in the air is v and the velocity of wind is u.
1.
2.
3.
4.
A spotlight (source) is fixed 4 m from the vertical wall and is rotating at rate 1 rad/s. The spot (image) moves horizontally on the wall. The speed of the spot on the wall, when the spotlight makes the angle of 45° with the wall, is (The line joining spot source and image is in the horizontal plane)
(1) 2 m/s
(2) 3 m/s
(3) 8 m/s
(4) 1 m/s
A projectile is projected from the ground such that 2 seconds before it reaches the highest point, its initial velocity makes an angle of 37° with vertical. Then the velocity of the projectile at the highest point is:
(1) 5 m/s
(2) 10 m/s
(3) 15 m/s
(4) 20 m/s
A ball is projected horizontally from the top of wall A of height 80 m with speed 10 m/s. At what distance from the wall ball hits the ground?
(1) 20 m
(2) 50 m
(3) 60 m
(4) 40 m
A swimmer swims a distance d upstream in 4 s and swims an equal distance downstream in 2 s. The ratio of swimmer's speed in still water to the speed of river water will be:
1.
2.
3.
4.
A particle starts from (-1, 0) in the x-y plane along a straight path making an angle of 60° with the X-axis. Which of the following will not be the coordinate through which the particle will pass?
(1) (0, )
(2) (1, 2)
(3) (2, 3)
(4) (4, 4)
An aeroplane flies \(400\) m north and then \(300\) m west and then flies \(1200\) m upwards. Its net displacement is:
1. | \(1200\) m | 2. | \(1300\) m |
3. | \(1400\) m | 4. | \(1500\) m |