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.  $\frac{\mathrm{l}}{\sqrt{{\mathrm{v}}^2 + {\mathrm{u}}^2}}$

2.  $\frac{2\mathrm{l}}{\sqrt{{\mathrm{v}}^2 - {\mathrm{u}}^2}}$

3.  $\frac{\mathrm{l}}{\sqrt{{\mathrm{v}}^2 - {\mathrm{u}}^2}}$

4.  $\frac{\mathrm{l}}{\mathrm{v} + \mathrm{u}}$

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.  $\frac{6}{5}$

2.  $\frac{3}{1}$

3.  $\frac{5}{3}$

4.  $\frac{4}{3}$

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, $\sqrt{3}$)

(2) (1, 2$\sqrt{3}$)

(3) (2, 3$\sqrt{3}$)

(4) (4, 4$\sqrt{3}$)

An aeroplane flies \(400\) m north and then \(300\) m west and then flies \(1200\) m upwards. Its net displacement is:

A projectile is thrown with an initial velocity (${\mathrm{v}}_{\mathrm{x}}\hat{\mathrm{i}} + {\mathrm{v}}_{\mathrm{y}}\hat{\mathrm{j}}$)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 $\frac{{\mathrm{v}}_{\mathrm{y}}}{{\mathrm{v}}_{\mathrm{x}}}$ 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 $3 \mathrm{m}/{\mathrm{s}}^2$, 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.  $\frac{2{\mathrm{v}}^2}{\mathrm{\pi r}}$

2.  $\frac{4{\mathrm{v}}^2}{3\mathrm{\pi r}}$

3.  $\frac{4{\mathrm{v}}^2}{7\mathrm{\pi r}}$

4.  $\frac{2{\mathrm{v}}^2}{7\mathrm{\pi r}}$