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Rain is falling vertically downwards with a speed of \(4\) kmh^-1. A girl moves a straight road with a velocity of \(3\) kmh^-1 . The apparent velocity of rain with respect to the girl is:
1. \(3\) kmh^-1
2. \(4\) kmh^-1
3. \(5\) kmh^-1
4. \(7\) kmh^-1
 

Ship \(A\) is travelling with a velocity of \(5~\mathrm{km/h}\) due east. A second ship is heading $\mathrm{}$\(30^\circ\) east of north. What should be the speed of second ship if it is to remain always due north with respect to the first ship?
1. \(10~\mathrm{km/h}\)
2. \(9~\mathrm{km/h}\)
3. \(8~\mathrm{km/h}\)
4. \(7~\mathrm{km/h}\)

A man swims from a point A on one bank of a river of width 100m. When he swims perpendicular to the water current, he reaches the other bank 50 m downstream. The angle to the bank at which he should swim, to reach the directly opposite point B on the other bank is
                                           
1.  $10°$ upstream
2.  $20°$ upstream
3.  $30°$ upstream
4.  $60°$ upstream

A boat is moving with a velocity \(3\hat i+ 4\hat j\) with respect to ground. The water in the river is moving with a velocity \(-3\hat i- 4\hat j\) with respect to the ground. The relative velocity of the boat with respect to water is:
1. \(8\hat j\)
2. \(-6\hat i-8\hat j\)
3. \(6\hat i + 8\hat j\)
4. \(5\sqrt{2}\)

The ratio of the distance carried away by the water current, downstream, in crossing a river, by a person, making same angle with downstream and upstream is 2 : 1. The ratio of the speed of person to the water current cannot be less than
1.  1/3
2.  4/5
3.  2/5
4.  4/3

A particle is moving in a circle of radius r centered at O with constant speed v. What is the change in velocity in moving from A to B ($\angle \mathrm{AOB}=40°$)?
1.  $2\mathrm{v} \sin 20°$
2.  $4\mathrm{v} \sin 40°$
3.  $2\mathrm{v} \sin 40°$
4.  $\mathrm{v} \sin 20°$

During a projectile motion, if the maximum height equals the horizontal range, then the angle of projection with the horizontal is:
1.  ${\tan }^{-1} \left(1\right)$
2.  ${\tan }^{-1} \left(2\right)$
3.  ${\tan }^{-1} \left(3\right)$
4.  ${\tan }^{-1} \left(4\right)$

Two bullets are fired horizontally with different velocities from the same height. Which will reach the ground first?

A grasshopper can jump a maximum distance 1.6 m. It spends negligible time on the ground. How far can it go in 10s?
1.  $5\sqrt{2} \mathrm{m}$
2.  $10\sqrt{2} \mathrm{m}$
3.  $20\sqrt{2} \mathrm{m}$
4.  $40\sqrt{2} \mathrm{m}$

A projectile is thrown in the upward direction making an angle of $60°$ with the horizontal direction with a velocity of $150 {\mathrm{ms}}^{-1}$. Then the time after which its inclination with the horizontal is $45°$ is
1.  $15\left(\sqrt{3}-1\right) \mathrm{s}$
2.  $15\left(\sqrt{3}+1\right) \mathrm{s}$
3.  $7.5\left(\sqrt{3}-1\right) \mathrm{s}$
4.  $7.5\left(\sqrt{3}+1\right) \mathrm{s}$

A number of bullets are fired in all possible directions with the same initial velocity $\mathrm{u}$. The maximum area of ground covered by bullets is
1.  $\mathrm{\pi }{\left(\frac{{\mathrm{u}}^2}{\mathrm{g}}\right)}^2$
2.  $\mathrm{\pi }{\left(\frac{{\mathrm{u}}^2}{2\mathrm{g}}\right)}^2$
3.  $\mathrm{\pi }{\left(\frac{\mathrm{u}}{\mathrm{g}}\right)}^2$
4.  $\mathrm{\pi }{\left(\frac{\mathrm{u}}{2\mathrm{g}}\right)}^2$

A hose lying on the ground shoots a stream of water upward at an angle of $60°$ to the horizontal with the velocity of $16 {\mathrm{ms}}^{-1}$. The height at which the water strikes the wall 8m away is
1. 8.9 m
2. 10.9 m
3. 12.9 m
4. 6.9 m

A rifle shoots a bullet with a muzzle velocity of 400 ms^-1 at a small target 400 m away. The height above the target at which the bullet must be aimed to hit the target is (g=10 ms^-2).
1.  1 m
2.  5 m
3.  10 m
4.  0.5 m

A projectile is given an initial velocity of \(\hat{i}+2\hat{j}.\) The cartesian equation of its path is: (Take \(g=10\) ms^-2).
1. \(y=2x-5x^2\)
2. \(y=x-5x^2\)
3. \(4y=2x-5x^2\)
4. \(y=2x-25x^2\)

In Fig. 5.201, the time taken by the projectile to reach from A to B is t. Then the distance AB is equal to
                     
1.  $\frac{\mathrm{ut}}{\sqrt{3}}$
2.  $\frac{\sqrt{3}\mathrm{ut}}{2}$
3.  $\sqrt{3}\mathrm{ut}$
3.  $2\mathrm{ut}$

A body is moving in a circle with a speed of 1 ms^-1. This speed increases at a constant rate of 2 ms^-1 every second. Assume that the radius of the circle described is 25 m. The total acceleration of the body after 2 s is
1.  $2 {\mathrm{ms}}^{-2}$
2.  $25 {\mathrm{ms}}^{-2}$
3.  $\sqrt{5} {\mathrm{ms}}^{-2}$
4.  $\sqrt{7} {\mathrm{ms}}^{-2}$

A projectile is thrown with velocity v at an angle $\mathrm{\theta }$ with the horizontal. When the projectile is at a height equal to half of the maximum height,
The vertical component of the velocity of the projectile is
1.  $3\mathrm{v} \sin \mathrm{\theta }$
2.  $\mathrm{v} \sin \mathrm{\theta }$
3.  $\frac{\mathrm{v} \sin \mathrm{\theta }}{\sqrt{2}}$
4.  $\frac{\mathrm{v} \sin \mathrm{\theta }}{\sqrt{3}}$

A projectile is thrown with velocity v at an angle $\mathrm{\theta }$ with the horizontal. When the projectile is at a height equal to half of the maximum height,
The velocity of the projectile when it is at a height equal to half of the maximum height is
1.  $\mathrm{v}\sqrt{{\cos }^2 \mathrm{\theta }+\frac{{\sin }^2 \mathrm{\theta }}{2}}$
2.  $\sqrt{2} \mathrm{v} \cos \mathrm{\theta }$
3.  $\sqrt{2} \mathrm{v} \sin \mathrm{\theta }$
4.  $\mathrm{v} \tan \mathrm{\theta } \sec \mathrm{\theta }$

A projectile is thrown with velocity v at an angle $\mathrm{\theta }$ with the horizontal. When the projectile is at a height equal to half of the maximum height,
What is the angle of projectile with the vertical if the velocity at the highest point is $\sqrt{2/5}$ times the velocity when it is at a height equal to half of the maximum height?
1.  $15°$
2.  $30°$
3.  $45°$
4.  $60°$