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A river is flowing with a speed of 1 km/hr. A swimmer wants to go to point 'C' starting from 'A'. He swims with a speed of 5 km/hr, at an angle $\theta$ with respect to the river. If AB=BC=400m. Then-

(1) time taken by the man is 12 min
(2) time taken by the man is 8 min
(3) the value of $\theta$ is 45$°$
(4) the value of $\theta$ is 53$°$

A particle starts from the origin at t=0 and moves in the x-y plane with constant acceleration 'a' in the y direction. Its equation of motion is $y=b{x}^2$. The x component of its velocity (at t=0) is:
(1) variable
(2) $\sqrt{\frac{2a}{b}}$
(3) $\frac{a}{2b}$
(4) $\sqrt{\frac{a}{2b}}$

A particle has initial velocity $\left(3\hat{\mathrm{i}}+4\hat{\mathrm{j}}\right)$ and has acceleration $\left(0.4\hat{\mathrm{i}}+0.3\hat{\mathrm{j}}\right)$. Its speed after 10 s:
1. 7 units
2. $7\sqrt{2}$ units
3. 8.5 units
4. 10 units

A boat is sent across a river in perpendicular direction with a velocity of 8 km/hr. If the resultant velocity of boat is 10 km/hr, then velocity of the river is : 
(1) 10 km/hr
(2) 8 km/hr
(3) 6 km/hr
(4) 4 km/hr

A train is moving towards east and a car is along north, both with same speed. The observed direction of car to the passenger in the train is 
(1) East-north direction
(2) West-north direction
(3) South-east direction
(4) None of these

If the body is moving in a circle of radius r with a constant speed v, its angular velocity is:
1. v²/r
2. vr
3. v/r
4. r/v

A motorcyclist going round in a circular track at a constant speed has:
(1) constant linear velocity.
(2) constant acceleration.
(3) constant angular velocity.
(4) constant force.

A particle moves with constant angular velocity in a circle. During the motion its:

The angular speed of a flywheel making 120 revolutions/minute is: 
(1) $2\pi rad/s$
(2) $4{\pi }^{2}rad/s$
(3) $\pi rad/s$
(4) $4\pi rad/s$

What is the value of linear velocity if \(\overset{\rightarrow}{\omega} = 3\hat{i} - 4\hat{j} + \hat{k}\) and \(\overset{\rightarrow}{r} = 5\hat{i} - 6\hat{j} + 6\hat{k}\)  :

The angle turned by a body undergoing circular motion depends on time as $\theta ={\theta }_0+{\theta }_{1}t+{\theta }_2{t}^2$. Then the angular acceleration of the body is 
(1) θ₁
(2) θ₂
(3) 2θ₁
(4) 2θ₂

A bomb is dropped from an aeroplane moving horizontally at constant speed. When air resistance is taken into consideration, the bomb 
(1) Falls to earth exactly below the aeroplane
(2) Fall to earth behind the aeroplane
(3) Falls to earth ahead of the aeroplane
(4) Flies with the aeroplane

If a body A of mass M is thrown with a velocity v at an angle of 30° to the horizontal and another body B of the same mass is thrown with the same speed at an angle of 60° to the horizontal. The ratio of horizontal range of A to B will be 
(1) 1 : 3
(2) 1 : 1
(3) $1:\sqrt{3}$
(4) $\sqrt{3}:1$

Which of the following sets of factors will affect the horizontal distance covered by an athlete in a long–jump event?
1. speed before he jumps and his weight
2. the direction in which he leaps and the initial speed
3. the force with which he pushes the ground and his speed
4. none of the above

The equation of motion of a projectile is given by x = 36 t metre and 2y = 96 t – 9.8 t² metre. The angle of projection is:
1. ${\sin }^{-1}\left(\frac{{\displaystyle 4}}{{\displaystyle 5}}\right)$
2. ${\sin }^{-1}\left(\frac{{\displaystyle 3}}{{\displaystyle 5}}\right)$
3. ${\sin }^{-1}\left(\frac{{\displaystyle 4}}{{\displaystyle 3}}\right)$
4. ${\sin }^{-1}\left(\frac{{\displaystyle 3}}{{\displaystyle 4}}\right)$

For a given velocity, a projectile has the same range of R for two angles of projection. If t₁ and t₂ are the times of flight in the two cases then:
(1) $t_1{t}_2\propto R^2$
(2) $t_1{t}_2\propto R$
(3) $t_1{t}_2\propto \frac{1}{R}$
(4) $t_1{t}_2\propto \frac{1}{R^2}$

A cricketer can throw a ball to a maximum horizontal distance of 100 m. With the same effort, he throws the ball vertically upwards. The maximum height attained by the ball is 
1. 100 m
2. 80 m
3. 60 m
4. 50 m

Neglecting the air resistance, the time of flight of a projectile is determined by:
(1) U_vertical
(2) U_horizontal
(3) U = U²_vertical + U²_horizontal
(4) U = U(U²_vertical + U²_horizontal )^1/2

A stone is thrown at an angle θ with the horizontal reaches a maximum height of H. Then the time of flight of stone will be:
(1) $\sqrt{\frac{2H}{g}}$
(2) $2\sqrt{\frac{2H}{g}}$
(3) $\frac{2\sqrt{2H\sin \theta }}{g}$
(4) $\frac{\sqrt{2H\sin \theta }}{g}$

The horizontal range of a projectile is $4\sqrt{3}$ times its maximum height. Its angle of projection will be:
1. 45°
2. 60°
3. 90°
4. 30°

A car is moving in a circular horizontal track of radius 10 m with a constant speed of 10 m/sec. A plumb bob is suspended from the roof of the car by a light rigid rod of length 1.00 m. The angle formed by the rod with respect to the vertical is:

Figure shows four paths for a kicked football. Ignoring the effects of air on the flight, rank the paths according to initial horizontal velocity component, highest first

(1) 1, 2, 3, 4
(2) 2, 3, 4, 1
(3) 3, 4, 1, 2
(4) 4, 3, 2, 1

A man standing on a road holds his umbrella at 30° with the vertical to keep the rain away. He throws the umbrella and starts running at 10 km/hr. He finds that raindrops are hitting his head vertically, the speed of raindrops with respect to the road will be:
(1) 10 km/hr
(2) 20 km/hr
(3) 30 km/hr
(4) 40 km/hr

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

A river is flowing from east to west at a speed of 5 m/min. A man on south bank of river, capable of swimming 10m/min in still water, wants to swim across the river in shortest time. He should swim:
1. Due north
2. Due north-east
3. Due north-east with double the speed of the river
4. None of the above

A person, aiming to reach the exact opposite point on the other bank of a stream, is swimming with a speed of 0.5 m/s at an angle of 120⁰ with the direction of flow of water. The speed of water in the stream is:
1. 1 m/s
2. 0.5 m/s
3. 0.25 m/s
4. 0.433 m/s

A man sitting in a bus travelling in a direction from west to east with a speed of 40 km/h observes that the rain-drops are falling vertically downwards. To another man standing on ground the rain will appear 
1. To fall vertically downwards
2. To fall at an angle going from west to east
3. To fall at an angle going from east to west
4. The information given is insufficient to decide the direction of the rain

A boat takes two hours to travel 8 km and back in still water. If the velocity of water is 4 km/h, the time taken for going upstream 8 km and coming back is 
(1) 2h
(2) 2h 40 min
(3) 1h 20 min
(4) Cannot be estimated with the information given

A 120 m long train is moving towards west with a speed of 10 m/s. A bird flying towards east with a speed of 5 m/s crosses the train. The time taken by the bird to cross the train will be 
(1) 16 sec
(2) 12 sec
(3) 10 sec
(4) 8 sec

A particle moves towards east with velocity 5 m/s. After 10 seconds its direction changes towards north with same velocity. The average acceleration of the particle is 
(1) Zero
(2) $\frac{1}{\sqrt{2}}m/s^{2}N-W$
(3) $\frac{1}{\sqrt{2}}m/s^{2}N-E$
(4) $\frac{1}{\sqrt{2}}m/s^{2}S-W$

Two trains along the same straight rails moving with constant speed 60 km/hr and 30 km/hr respectively towards each other. If at time t = 0, the distance between them is 90 km, the time when they collide is:
1. 1 hr
2. 2 hr
3. 3 hr
4. 4 hr

To a person, going eastward in a car with a velocity of 25 km/hr, a train appears to move towards north with a velocity of $25\sqrt{3}$ km/hr. The actual velocity of the train will be
(1) 25 km/hr
(2) 50 km/hr
(3) 5 km/hr
(4) $5\sqrt{3}$ km/hr

The \(x\) and \(y\) coordinates of the particle at any time are \(x = 5t-2t^2\) and \(y=10t\) respectively, where \(x\) and \(y\) are in metres and \(t\) is in seconds. The acceleration of the particle at \(t=2\) s is:
1. \(0\)
2. \(5\) m/s²
3.  \(-4\) m/s²
4.  \(-8\) m/s²

A ship A is moving Westwards with a speed of 10 km h^-1 and a ship B 100 km South of A, is moving Northwards with a speed of 10 km h^-1. The time after which the distance between them becomes shortest is
1., h
2. 5h
3. 5$\sqrt{2}$h
4. 10$\sqrt{2}$h

The velocity of a projectile at the initial point A is (2i + 3j) m/s. Its velocity (in m/s) at point B is:

1.  -2i+3j
2.  -2i-3j
3.   2i-3j
4.  2i+3j

A body is moving with velocity 30 m/s towards east. After 10 s its velocity becomes 40 m/s towards north. The average acceleration of the body is
(1) $7 \mathrm{m}/{\mathrm{s}}^2$                                             
(2) $\sqrt{7} \mathrm{m}/{\mathrm{s}}^2$
(3) $5 \mathrm{m}/{\mathrm{s}}^2$                                             
(4) $1 \mathrm{m}/{\mathrm{s}}^2$

A missile is fired for maximum range with an initial velocity of 20 m/s. If g=10 $\mathrm{m}/{\mathrm{s}}^2$, the range of the missile is:
1. 50 m                                                          2. 60 m
3. 20 m                                                          4. 40 m

A projectile is fired at an angle of 45$°$ with the horizontal. The elevation angle $\alpha$ of the projectile at its highest point as seen from the point of projection is:
1. 60$°$                                           2. ${\tan }^{-1}\left(\frac{1}{2}\right)$
3. ${\tan }^{-1}\left(\frac{\sqrt{3}}{2}\right)$                               4. $45°$

The speed of a boat is 5 km/h in still water. It crosses a river of width 1.0 km along the shortest possible path in 15 min.  The velocity (in km $h^{-1}$) of the river water is
(1) 5
(2) 1
(3) 3
(4) 4

If a unit vector is represented by $0.5\hat{i}+0.8\hat{j}+c\hat{k}$ the value of c is 
(1) 1
(2) $\sqrt{0.11}$
(3) $\sqrt{0.01}$
(4) 0.39

A person swims in a river aiming to reach exactly opposite point on the banks of a river. His speed of swimming is 0.5 m $s^{-1}$ at an angle $120°$ with the direction of flow of water. The speed of water in stream is -
(1) 1.0 m$s^{-1}$
(2) 0.5 m $s^{-1}$
(3) 0.25 m$s^{-1}$
(4) 0.43 m$s^{-1}$

Two particles are projected with same initial velocities at an angle $30° and 60°$ with the horizontal. Then
(1) their heights will be equal
(2) their ranges will be equal
(3) their time of flights will be equal
(4) their ranges will be different

If a vector $2\hat{i}+3\hat{j}+8\hat{k}$ is perpendicular to the vector $4\hat{j}-4\hat{i}+\alpha \hat{k}$ then the value of $\alpha$ is 
(1) -1
(2) $\frac{-1}{2}$
(3) $\frac{1}{2}$
(4) 1

A stone tied to the end of a string of 1 m long is whirled in a horizontal circle with a constant speed. If the stone makes 22 revolutions in 44 s, what is the magnitude and direction of acceleration of the stone?
(1) ${\mathrm{\pi }}^2{\mathrm{ms}}^{-2}$ and direction along the tangent to the circle.
(2) ${\mathrm{\pi }}^2{\mathrm{ms}}^{-2}$ and direction along the radius towards the centre.
(3) $\frac{{\mathrm{\pi }}^2}{4}m{s}^{-2}$ and direction along the radius towards the centre.
(4) ${\mathrm{\pi }}^2{\mathrm{ms}}^{-2}$ and direction along the radius away from the centre.

A particle of mass m is projected with velocity v making an angle of $45°$ with the horizontal. When the particle lands on the ground level the magnitude of the change in its momentum will be
(1) zero
(2) 2 mv
(3) mv / $\sqrt{2}$
(4) mv$\sqrt{2}$