JEE Main Motion in a Plane Practice Questions With Solutions

The angle of projection for a projectile to have same horizontal range and maximum height is :

The co-ordinates of a particle moving in $x$x-$y$y plane are given by : $x=2+4\mathrm{t},y=3\mathrm{t}+8{\mathrm{t}}^2$x = 2 + 4 t , y = 3 t + 8 t^{2}.

The motion of the particle is :

Position of an ant ($\mathrm{S}$S in metres) moving in $\mathrm{Y}$Y-$\mathrm{Z}$Z plane is given by $S=2t^2\hat{j}+5\hat{k}$S = 2 t^{2} \hat{j} + 5 \hat{k} (where $t$t is in second). The magnitude and direction of velocity of the ant at $\mathrm{t}=1\mathrm{s}$t = 1 \textrm{ } s will be :

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

Two projectiles are projected at ${30}^{\circ }$30^{\circ} and ${60}^{\circ }$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${}^{\circ }$^{\circ} with horizontal is 50 m. If the projectile is projected with same velocity at an angle of 45${}^{\circ }$^{\circ} with horizontal, then its range will be

The trajectory of projectile, projected from the ground is given by $y=x-\frac{x^2}{20}$y = x - \frac{x^{2}}{20}. Where $x$x and $y$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}$40 \textrm{ } m / s and $60\mathrm{m}/\mathrm{s}$60 \textrm{ } m / s at angles ${30}^{\circ }$30^{\circ} and ${60}^{\circ }$60^{\circ} with the horizontal respectively. The ratio of their ranges respectively is $(g=10\mathrm{m}/{\mathrm{s}}^2)$\left(\right. g = 10 \textrm{ } m / s^{2} \left.\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 }$45^{\circ}, it's range is maximum.

Reason R : For maximum range, the value of $\sin 2\theta$sin ⁡ 2 \theta should be equal to one.

In the light of the above statements, choose the correct answer from the options given below:

A child stands on the edge of the cliff $10\mathrm{m}$10 \textrm{ } m above the ground and throws a stone horizontally with an initial speed of $5{\mathrm{ms}}^{-1}$5 \left(\textrm{ } ms\right)^{- 1}. Neglecting the air resistance, the speed with which the stone hits the ground will be ${\mathrm{ms}}^{-1}$ms^{- 1} (given, $g=10{\mathrm{ms}}^{-2}$g = 10 \left(\textrm{ } ms\right)^{- 2} ).