Two objects are projected with same velocity 'u' however at different angles $$\alpha$$ and $$\beta$$ with the horizontal. If $$\alpha +\beta =90^{\circ }$$, the ratio of horizontal range of the first object to the 2nd object will be :

The maximum vertical height to which a man can throw a ball is 136 m. The maximum horizontal distance upto which he can throw the same ball is :

A projectile is projected at $$30^{\circ }$$ from horizontal with initial velocity $$40{\mathrm{ms}}^{-1}$$. The velocity of the projectile at $$\mathrm{t}=2\mathrm{s}$$ from the start will be : (Given $$g=10\mathrm{m}/{\mathrm{s}}^2$$ )

Two projectiles are projected at $$30^{\circ }$$ and $$60^{\circ }$$ with the horizontal with the same speed. The ratio of the maximum height attained by the two projectiles respectively is:

The range of the projectile projected at an angle of 15$${}^{\circ }$$ with horizontal is 50 m. If the projectile is projected with same velocity at an angle of 45$${}^{\circ }$$ with horizontal, then its range will be

The trajectory of projectile, projected from the ground is given by $$y=x-\frac{x^2}{20}$$. Where $$x$$ and $$y$$ are measured in meter. The maximum height attained by the projectile will be.

Two projectiles A and B are thrown with initial velocities of $$40\mathrm{m}/\mathrm{s}$$ and $$60\mathrm{m}/\mathrm{s}$$ at angles $$30^{\circ }$$ and $$60^{\circ }$$ with the horizontal respectively. The ratio of their ranges respectively is $$\left(g=10\mathrm{m}/{\mathrm{s}}^2\right)$$

Given below are two statements : one is labelled as Assertion A and the other is labelled as Reason R Assertion A : When a body is projected at an angle $$45^{\circ }$$, it's range is maximum. Reason R : For maximum range, the value of $$\sin 2\theta$$ should be equal to one. In the light of the above statements, choose the correct answer from the options given below:

An object moves with speed $$v_1,v_2$$ and $$v_3$$ along a line segment AB, BC and CD respectively as shown in figure. Where AB = BC and AD = 3AB, then average speed of the object will be:

A vehicle travels $4\mathrm{km}$ with speed of $3\mathrm{km}/\mathrm{h}$ and another $4\mathrm{km}$ with speed of $5\mathrm{km}/\mathrm{h}$, then its average speed is

Match Column-I with Column-II : .tg {border-collapse:collapse;border-spacing:0;} .tg td{border-color:black;border-style:solid;border-width:1px;font-family:Arial, sans-serif;font-size:14px; overflow:hidden;padding:10px 5px;word-break:normal;} .tg th{border-color:black;border-style:solid;border-width:1px;font-family:Arial, sans-serif;font-size:14px; font-weight:normal;overflow:hidden;padding:10px 5px;word-break:normal;} .tg .tg-7btt{border-color:inherit;font-weight:bold;text-align:center;vertical-align:top} .tg .tg-0pky{border-color:inherit;text-align:left;vertical-align:top} Column-I ($$x$$-t graphs) Column-II ($$v$$-t graphs) A. I. B. II. C. III. D. IV. Choose the correct answer from the options given below:

The distance travelled by a particle is related to time t as $$x=4{\mathrm{t}}^2$$. The velocity of the particle at t=5s is :-

A car travels a distance of '$$x$$' with speed $$v_1$$ and then same distance '$$x$$' with speed $$v_2$$ in the same direction. The average speed of the car is :

The velocity time graph of a body moving in a straight line is shown in the figure. The ratio of displacement to distance travelled by the body in time 0 to 10s is :

The position of a particle related to time is given by $x=\left(5t^2-4t+5\right)\mathrm{m}$. The magnitude of velocity of the particle at $t=2 s$ will be :

The distance travelled by an object in time $$t$$ is given by $$s=(2.5)t^2$$. The instantaneous speed of the object at $$\mathrm{t}=5\mathrm{s}$$ will be:

A passenger sitting in a train A moving at $$90\mathrm{km}/\mathrm{h}$$ observes another train $$\mathrm{B}$$ moving in the opposite direction for $$8\mathrm{s}$$. If the velocity of the train B is $$54\mathrm{km}/\mathrm{h}$$, then length of train B is:

Two trains 'A' and 'B' of length '$$l$$' and '$$4l$$' are travelling into a tunnel of length '$$\mathrm{L}$$' in parallel tracks from opposite directions with velocities $$108\mathrm{km}/\mathrm{h}$$ and $$72\mathrm{km}/\mathrm{h}$$, respectively. If train 'A' takes $$35\mathrm{s}$$ less time than train 'B' to cross the tunnel then. length '$$L$$' of tunnel is : (Given $$\mathrm{L}=60l$$ )

A ball is thrown vertically upward with an initial velocity of $$150\mathrm{m}/\mathrm{s}$$. The ratio of velocity after $$3\mathrm{s}$$ and $$5\mathrm{s}$$ is $$\frac{x+1}{x}$$. The value of $$x$$ is ___________. $$\{$$ take, $$g=10\mathrm{m}/{\mathrm{s}}^2\}$$

From the $$\mathrm{v}-t$$ graph shown, the ratio of distance to displacement in $$25\mathrm{s}$$ of motion is: