A projectile is launched at an angle '$$\alpha$$' with the horizontal with a velocity 20 ms$$-$$1. After 10 s, its inclination with horizontal is '$$\beta$$'. The value of tan$$\beta$$ will be : (g = 10 ms$$-$$2).

A girl standing on road holds her umbrella at 45$${}^{\circ }$$ with the vertical to keep the rain away. If she starts running without umbrella with a speed of 15$$\sqrt{2}$$ kmh$$-$$1, the rain drops hit her head vertically. The speed of rain drops with respect to the moving girl is :

Given below are two statements. One is labelled as Assertion A and the other is labelled as Reason R. Assertion A : Two identical balls A and B thrown with same velocity 'u' at two different angles with horizontal attained the same range R. IF A and B reached the maximum height h1 and h2 respectively, then $$R=4\sqrt{h_1{h}_2}$$ Reason R : Product of said heights. {h_1}{h_2} = \left( {{{{u^2}{{\sin }^2}\theta } \over {2g}}} \right)\,.\,\left( {{{{u^2}{{\cos }^2}\theta } \over {2g}}} \right) Choose the correct answer :

A projectile is projected with velocity of 25 m/s at an angle $$\theta$$ with the horizontal. After t seconds its inclination with horizontal becomes zero. If R represents horizontal range of the projectile, the value of $$\theta$$ will be : [use g = 10 m/s2]

At t = 0, truck, starting from rest, moves in the positive x-direction at uniform acceleration of 5 ms$$-$$2. At t = 20 s, a ball is released from the top of the truck. The ball strikes the ground in 1 s after the release. The velocity of the ball, when it strikes the ground, will be : (Given g = 10 ms$$-$$2)

Two projectiles P1 and P2 thrown with speed in the ratio $$\sqrt{3}$$ : $$\sqrt{2}$$, attain the same height during their motion. If P2 is thrown at an angle of 60$${}^{\circ }$$ with the horizontal, the angle of projection of P1 with horizontal will be :

A ball is projected from the ground with a speed 15 ms$$-$$1 at an angle $$\theta$$ with horizontal so that its range and maximum height are equal, then 'tan $$\theta$$' will be equal to :

Two projectiles thrown at $$30^{\circ }$$ and $$45^{\circ }$$ with the horizontal respectively, reach the maximum height in same time. The ratio of their initial velocities is :

Two projectiles are thrown with same initial velocity making an angle of $$45^{\circ }$$ and $$30^{\circ }$$ with the horizontal respectively. The ratio of their respective ranges will be :

At time $$t=0$$ a particle starts travelling from a height $$7\hat{z}\mathrm{cm}$$ in a plane keeping z coordinate constant. At any instant of time it's position along the $$\hat{x}$$ and $$\hat{y}$$ directions are defined as $$3\mathrm{t}$$ and $$5{\mathrm{t}}^3$$ respectively. At t = 1s acceleration of the particle will be

Two balls A and B are placed at the top of 180 m tall tower. Ball A is released from the top at t = 0 s. Ball B is thrown vertically down with an initial velocity 'u' at t = 2 s. After a certain time, both balls meet 100 m above the ground. Find the value of 'u' in ms$$-$$1. [use g = 10 ms$$-$$2] :

A small toy starts moving from the position of rest under a constant acceleration. If it travels a distance of 10m in t s, the distance travelled by the toy in the next t s will be :

Two buses P and Q start from a point at the same time and move in a straight line and their positions are represented by $$X_P(t)=\alpha t+\beta t^2$$ and $$X_Q(t)=ft-t^2$$. At what time, both the buses have same velocity?

A bullet is shot vertically downwards with an initial velocity of $$100\mathrm{m}/\mathrm{s}$$ from a certain height. Within 10 s, the bullet reaches the ground and instantaneously comes to rest due to the perfectly inelastic collision. The velocity-time curve for total time $$\mathrm{t}=20\mathrm{s}$$ will be: (Take g = 10 m/s2).

The velocity of the bullet becomes one third after it penetrates 4 cm in a wooden block. Assuming that bullet is facing a constant resistance during its motion in the block. The bullet stops completely after travelling at (4 + x) cm inside the block. The value of x is :

A NCC parade is going at a uniform speed of $$9\mathrm{km}/\mathrm{h}$$ under a mango tree on which a monkey is sitting at a height of $$19.6\mathrm{m}$$. At any particular instant, the monkey drops a mango. A cadet will receive the mango whose distance from the tree at time of drop is: (Given $$g=9.8\mathrm{m}/{\mathrm{s}}^2$$ )

A ball is thrown up vertically with a certain velocity so that, it reaches a maximum height h. Find the ratio of the times in which it is at height $$\frac{h}{3}$$ while going up and coming down respectively.

If $$\mathrm{t}=\sqrt{x}+4$$, then $${\left(\frac{\mathrm{d}x}{\mathrm{d}t}\right)}_{\mathrm{t}=4}$$ is :

A juggler throws balls vertically upwards with same initial velocity in air. When the first ball reaches its highest position, he throws the next ball. Assuming the juggler throws n balls per second, the maximum height the balls can reach is

A ball is released from a height h. If $$t_1$$ and $$t_2$$ be the time required to complete first half and second half of the distance respectively. Then, choose the correct relation between $$t_1$$ and $$t_2$$.