Relative Velocity

Q.

A police van moving on a highway with a speed of 30 km/ h fires a bullet at a thief’s car speeding away in the same direction with a speed of 192 km/ h. If the muzzle speed of the bullet is 150 m s–1, at what speed does the bullet hit the thief’s car? (Note: Obtain that speed which is relevant for damaging the thief’s car).

Q.

Train $A$ and train $B$ are running on parallel tracks in opposite directions with speeds of $36km/hour$ and $72km/hour$, respectively. A person is walking in train $A$ in the direction opposite to its motion with a speed of $1.8km/hour$. Speed (in $m{s}^{-1}$) of this person as observed from train $B$ will be close to:

1. $29.5m{s}^{-1}$

2. $30.5m{s}^{-1}$

3. $31.5m{s}^{-1}$

4. $28.5m{s}^{-1}$

Q. O. The position of a particle moving in a straight line is given by y=3t^3+ t^2+5 (where y is in cm and t is in second), then find the acceleration of the particle at time t=2 s

Q. The speed at the maximum height of a projectile is half of its initial speed of projection (u). The horizontal range of the projectile is

Q. the speed of a projectile at its maximum height is half of its initial speed. the angle of projection is?

Q. A particle is moving on a straight line such that velocity is given by v= 6t + 3t² , where v is in m/s and t is in second. If at t=0, the particle is at origin then average velocity during t=0 to t=3 s is.

Q. 20.A projectile is fired vertically upwards from the surface of the earth with a velocity Ive, where be is the escape velocity and k<1.If R is the radius of the earth, the maximum height to which it will rise , measured from the center of the earth, wii be (Neglect air resistance)

Q. 72.A block slides down an inclined plane of slope of angle theta with a constant velocity v. it is then projected up the plane with an initial velocity u, The distance upto which it will rise before coming to rest is

Q. 21 A body moving with uniform acceleration is having velocity 2 m/s and 8 m/s at t = 1 s and t = 4 s respectively. Then average velocity of particle in the time interval t = 1 s to t 4 s is (1) 2 m/s (2) 3 m/s (4) 5 m/s (3) 5/3 m/s

Q. A rocket is launched with velocity 10 km/s. If radius of earth is R, then maximum height attained by it will be- (1) 2R (2) 3R (3) 4R (4) 5

Q. Escape velocity of an atmospheric particle which is 1000 km above the earths surface, is (radius of earth is6400 km and g =9.8 m/s2)17(1) 6.5 km/s(2) 8 km/s(3) 10 km/s(4) 11.2 km/sTE

Q. A boy wants to jump from building A to building B. Height of building A is 25 m and that of building B is 5 m. Distance between buildings is 4 m. Assume that the boy jumps horizontally, then calculate minimum velocity with which he has to jump to land safely on building B. (1) 6 m/s (2) 8 m/s (3) 4 m/s (4) 2 m/s

Q. A ball is allowed to fall from rest from height h. If it travels 9/25th of total height in the last second of its fall then ball will hit ground will hit ground with speed (g=10m/s2) A:30ms B:35ms C: 45ms D: 50ms

Q. A man is walking on a road with a velocity $3\text{km/hr}$. Suddenly rain starts falling. The velocity of rain is $10\text{km/hr}$ in vertically downward direction. The relative velocity of the rain with respect to man is -

1. $\sqrt{13}\text{km/hr}$
2. $\sqrt{7}\text{km/hr}$
3. $\sqrt{109}\text{km/hr}$
4. $13\text{km/hr}$

Q. 16 m)4 A ball is thrown vertically upwards from the ground. It cosses a point at the height of 25 m twice at an interval of4 The ball was thrown with the velocity of

Q. A projectile is projected with a speed 30m/s at an angle 30^° with the vertical.the speed of the projectile when its direction of motion makes an angle 30^° with the horizontal i

Q. Two trains A and B are approaching each other with speed 30 km/hr. A bird flies to and fro between A and B with a speed of 60 km/hr until they collide. Find the distance covered and displacement of the bird?

1. distance = 120 km displacement = 0 km

2. distance = 60 km displacement = 0 km

3. distance = 60 km displacement = -30 km

4. distance = 60 km displacement = 30 km

Q. A rocket is launched vertical from the surface of the earth of radius R with initial speed v. If atmospheric resistance is neglected , then maximum height attained by the rocket is (1) h=R/ (2gR/v^2 -1) (2) h=R/ (2gR/v^2 +1) (3) h=R^2/ (2gR/v^2 -1) (4) h=R^2/ (2gR/v^2 +1)

Q.

Two parallel rail tracks run north-south. Train A moves north with a speed of 54 km/h and train B moves south with a speed of 90 km/hr. What is the velocity of a monkey running on the roof of the train A against its motion (with its velocity of 18 km/h with respect to the train A) as observed by a man standing on the ground?

1. 36 km/hr - North

2. 36 km/hr - South

3. 72 km/hr - North

4. 72 km/hr - South

Q. A ball rolls off the edge of a horizontal table top 4m high. If it strikes the floor at a point 5 m horizontally away from the edge of the table, what was its speed at the instant it left the table.

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Q. a projectile is fired vertically upward with escape velocity from earth .if it is fired at 45 to the horizontal what should be the sped so that it escape from te earth

Q.

A car travelling at 60 km/h overtake another car travelling at 42 km/h. Assuming each car to be 5m long, find the time taken during the overtake and the total road distance used for the overtake.

1. 2 sec

2. 1 sec

3. 10 sec

4. 5 sec

Q. define time of flight (Tf) and write the expression for it

Q. A spaceman in training is rotated in a seat at the end of a horizontal arm of length 5 m. if he can withstand acceleration upto 9g, then what is the maximum number of revouloution per sec permissible?

Q. a ball is dropped from a building of height 40m .simul†an eously another ball is thrown up with a speed 20 m/s .the relative speed of first ball w.r.t second ball at t=1s is(g=10m/s2)

Q.

A projectile is fired from the top of a 40 m high cliff with an initial speed of 50 m/s at an unknown angle. Find its speed when it hits the ground

1. None of these

2. 45 m/s

3. 58 m/s

4. 38 m/s

Q. A particle is projected on an incline plane having inclination 30^° , at an angle 30^° with the incline plane witha velocity 15 m/s. Range of the projectile on the incline plane will be

Q. If an object is moving with velocity 54km/h. What will be its velocity in m/s and km/min

Q. A bus with a vertical wind shield moves horizontalat a speed of 40 km/hr, while rain is fallingvertically at a speed of 30 km/hr. The angle atwhich rain drops strike the wind shield is(1) 37^° (2) 45^° (3) 53(4) 30^°

Q. two busescA and B are at position 50m andv100m from the orgin at time t=0 they start moving in the same direction simul†an eously with uniform velocity of 10m/s2 and 5m/s2 determine the time and position at which A overtake