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.