A projectile is fired vertically upwards with an initial velocity u. After an interval of T seconds a second projectile is fired vertically upwards, also with initial velocity u.

(1) They meet at time $t=\frac{u}{g}$ and at a height $\frac{u^2}{2g}+\frac{g{T}^2}{8}$

(2) They meet at time $t=\frac{u}{g}+\frac{T}{2}$ and at a height $\frac{u^2}{2g}+\frac{g{T}^2}{8}$

(3) They meet at time $t=\frac{u}{g}+\frac{T}{2}$ and at a height $\frac{u^2}{2g}-\frac{g{T}^2}{8}$

(4) They never meet

Two cars are moving in the same direction with the same speed \(30\) km/hr. They are separated by a distance of \(5\) km. The speed of a car moving in the opposite direction, if it meets these two cars at an interval of \(4\) minutes, will be:
1. \(40\) km/hr
2. \(45\) km/hr
3. \(30\) km/hr
4. \(15\) km/hr

A 150 m long train is moving to north at a speed of 10 m/s. A parrot flying towards south with a speed of 5 m/s crosses the train. The time taken by the parrot the cross to train would be: 

(1) 30 s

(2) 15 s

(3) 8 s

(4) 10 s

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

A bus is moving with a velocity 10 m/s on a straight road. A scooterist wishes to overtake the bus in 100 s. If the bus is at a distance of 1 km from the scooterist, with what velocity should the scooterist chase the bus

(1) 50 m/s

(2) 40 m/s

(3) 30 m/s

(4) 20 m/s

An automobile travelling with a speed of 60 km/h, can brake to stop within a distance of 20 m. If the car is going twice as fast, i.e. 120 km/h, the stopping distance will be 

(1) 20 m

(2) 40 m

(3) 60 m

(4) 80 m

A lift is going up. The total mass of the lift and the passenger is 1500 kg. The variation in the speed of the lift is as given in the graph. The height to which the lift takes the passenger is

(1) 3.6 meters

(2) 8 meters

(3) 1.8 meters

(4) 36 meters

A particle is projected upwards. The times corresponding to height \(h\) while ascending and while descending are t₁ and t₂ respectively. The velocity of projection will be:
1. \(gt_1\)
2. \(gt_2\)
3. \(g(t_1+t_2)\)
4. \(\frac{g(t_1+t_2)}{2}\)

A body falls freely from the top of a tower. It covers 36% of the total height in the last second before striking the ground level. The height of the tower is:

(1) 50 m

(2) 75 m

(3) 100 m

(4) 125 m

Two bodies are thrown simultaneously from a tower with same initial velocity v₀ : one vertically upwards, the other vertically downwards. The distance between the two bodies after time t is

(1) $2v_{0}t+\frac{1}{2}g{t}^2$

(2) 2v₀t

(3) $v_{0}t+\frac{1}{2}g{t}^2$

(4) v₀t