Particles P and Q are at →rP = 3ˆi + 2ˆj and →rQ = 2ˆi + ˆj. Their velocities at these positions are →vP = 2ˆi + 3ˆj and →vQ = 3ˆi + cˆj respectively. If they collide after one second, then the value of c is
(1) 1
(2) 2
(3) 3
(4) 4
Two projectiles are thrown at different angles but their ranges R are the same. If their times of flight are t1 and t2, then the product of their times of flight t1t2 is proportional to
1. 1R
2. 1R2
3. R2
4. R
It is raining at 20 m/s in still air. Now a wind starts blowing with speed 10 m/s in the north direction. If a cyclist starts moving at 10 m/s in the south direction, then the apparent velocity of rain with respect to a cyclist will be:
1. 20 m/s
2. 20√2 m/s
3. 10√5 m/s
4. 30 m/s
A body of mass 2 kg is projected at a speed of 20 m/s from a pillar of height 40 m at an angle of 30° with the horizontal in an upward direction. The speed with which it will hit the ground is
(1) 30 m/s
(2) 20√3 m/s
(3) 25 m/s
(4) 40 m/s
Path of a projectile with respect to another projectile so long as both remain in the air is:
1. Circular
2. Parabolic
3. Straight
4. Hyperbolic
A particle is thrown with velocity u making an angle θ with the horizontal. It just crosses the top of two poles each of height h after 1 s and 3 s respectively. The time of flight of the particle is:
(1) 4 s
(2) 2 s
(3) 8 s
(4) 6 s
A projectile is moving in the XY plane such that the horizontal and vertical directions are along the X-axis and Y-axis respectively. The projectile is fired from the origin at a large height with initial velocity (50ˆi + 20ˆj) m/s. The time after which instantaneous velocity of the projectile becomes perpendicular to its initial velocity is: (g=10m/s2)
(1) 7.5 s
(2) 14.5 s
(3) 5.5 s
(4) 10.5 s
A particle is thrown from the ground with a speed u at an angle θ above the horizontal. The rate of change of velocity of the particle at the highest point of the path is:
1. gsinθ
2. gcosθ
3. g
4. Zero
A missile is fired for maximum range with an initial velocity of 20 m/s, then the maximum height of missile is: (Take g=10 m/s2)
1. 20 m
2. 30 m
3. 10 m
4. 40 m
A particle is moving along a circle of radius R with constant speed v0. What is the magnitude of change in velocity when the particle goes from point A to B as shown?
1. | 2v0sinθ2 | 2. | v0sinθ2 |
3. | 2v0cosθ2 | 4. | v0cosθ2 |