\(5\) people are standing at the vertices of a regular pentagon of side \(a\). Each person moves towards the person standing at the adjacent corner with the same speed \(v\). Then the persons:
1. Meet at the centre of the pentagon at a time \(t = \frac{a}{v_1(1-\cos60^{\circ})}\).
2. Meet at the centre of the pentagon after covering a distance \( = \frac{a}{(1-\cos72^{\circ})}\).
3. Never meet.
4. Meet at the center of pentagon after time \(\frac{a}{v}\).

A particle revolves in a horizontal circle with decreasing velocity. The angle between instantaneous velocity and instantaneous acceleration of the particle at an instant is

(1) < 90°

(2) > 90°

(3) = 90°

(4) $\ge$ 90°

Two projectiles are thrown horizontally from a high cliff in the opposite direction with the same speed 20 m/ s simultaneously. At what time velocities of both particles become perpendicular?

(1) 2$\sqrt{2}$ s

(2) 2 s

(3) 4 s

(4) 4$\sqrt{2}$ s

The equation of the trajectory of a projectile is given as $\mathrm{y} = 4\mathrm{x} - \frac{1}{4}{\mathrm{x}}^2$. The range of the projectile is:

(1) 1 m

(2) 32 m

(3) 16 m

(4) 48 m

A cannon can give a maximum speed of 70 m/s to bombs. The maximum distance up to which cannon projects a bomb is (g = 10 m/${\mathrm{s}}^2$)

(1) 490 m

(2) 245 m

(3) 100 m

(4) 300 m

A man is running horizontally at a velocity of 6 m/s while rain is falling vertically at 6 m/s. The rain strikes the man with a speed of

(1) 6$\sqrt{2}$ m/s

(2) 3$\sqrt{3}$ m/s

(3) 6 m/s

(4) 18 m/s

A man wants to cross a river 600 m wide flowing at 8 m/s in the shortest time. Man has a speed of 6 m/ s in still water. What is the path length covered by the man in the river?

1. Infinite

2. 1 km

3. 100 m

4. 1000 cm

The trajectory of a projectile in the vertical plane is y = ax - ${\mathrm{bx}}^2$ where a and b are constants, x and y are horizontal and vertical displacements from point of projection. The angle of projection from the horizontal is

1.  ${\tan }^{-1} \left(\frac{\mathrm{a}}{\mathrm{b}}\right)$

2.  ${\tan }^{-1} \left(\mathrm{b}\right)$

3.  ${\tan }^{-1} \left(\frac{\mathrm{b}}{\mathrm{a}}\right)$

4.  ${\tan }^{-1} \left(\mathrm{a}\right)$

A shell is fired vertically upward with a velocity of \(20\) m/s from a trolley moving horizontally with a velocity of \(10\) m/s. A person on the ground observes the motion of the shell-like a parabola whose horizontal range is: (\(g= 10~\text{m/s}^2\)${\mathrm{}}^{}$)

A car is moving at a speed of 30 m/s on a horizontal circular track of radius of 300 m. This speed is increasing at a rate of 4 $\mathrm{m}/{\mathrm{s}}^2$. Total acceleration of the car is:

(1) 5 $\mathrm{m}/{\mathrm{s}}^2$

(2) 7 $\mathrm{m}/{\mathrm{s}}^2$

(3) 1 $\mathrm{m}/{\mathrm{s}}^2$

(4) 3 $\mathrm{m}/{\mathrm{s}}^2$