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 |
A projectile is thrown with an initial velocity ()m/s. Consider horizontal direction and vertical direction as x and y axes respectively. If the range of the projectile is double the maximum height, then is
(1) 4
(2) 3
(3) 2
(4) 1
A car is moving on a circular track at a speed of 20 m/s having a radius of 100 m. If it starts decelerating uniformly at the rate of , the angle made by the resultant acceleration with the direction of its instantaneous velocity is:
(1) 37°
(2) 127°
(3) 53°
(4) 143°
An object is moving on a circular path of the radius r with constant speed v. The average acceleration of the object, after it has travelled three and a half rounds, is
1.
2.
3.
4.
A swimmer can swim in still water at a speed of 5 m/s and takes , time to cross a river in the shortest time and shortest path respectively. If the speed of the river increases, the time is taken to cross the river in the shortest time and the shortest path be respectively. Then
1.
2.
3.
4.