Projectile Motion

Two projectiles are projected from same position under gravity at different angles with horizontal in the same vertical plane. If velocity of one with respect to other is $v,$ acceleration of one with respect to other is $a$ and position of one with respect to other is $r,$ then which of the following graphs is(are) correct?

A particle is projected from ground to ground and its path is as shown in the figure. Points $A$ and $B$ are at same horizontal level and points $C$ and $D$ are at another same horizontal level. Separation between line $AB$ and $CD$ is $5 \mathrm{m}.$ If particle takes time $t_1$ to go from $A$ to $B$ and time $t_2$ from $C$ to $D,$ then is $\left(g=10 \mathrm{m} {\mathrm{s}}^{-2}\right)$

A particle is projected with speed $10\sqrt{2} \mathrm{m} {\mathrm{s}}^{-1}$ from top of a tower of height $H$ as shown in figure
(take $H=10 \mathrm{m}$and $g=10 \mathrm{m} {\mathrm{s}}^{-2}$ ). Then

A projectile has the same range $R$ for two angles of projections. If $T_1$ and $T_2$ be the times of flight in the two cases, then (using $\theta$ as the angle of projection corresponding to $T_1$ )

Two particles are projected from same point with same initial speed $u$ at angles of projection $\alpha$ and $\beta .t_1$ and $t_2$ are their respective time of flights and $h_1$ and $h_2$ are their respective maximum heights. If they strike the horizontal ground at same point having range $R,$ then

A particle is moving in $X-Y$ plane on path $y=x^2-$ $2x+5.$ Its $x$ component of velocity is constant and is equal to $5 \mathrm{m} {\mathrm{s}}^{-1}.$ Acceleration of the particle at $x=2 \mathrm{m}$ is

For a projectile thrown at an angle $\theta$ with the horizontal ground, maximum range on the ground can be achieved by projecting at $\theta =$_____$°$. (In degrees)

Path of a projectile as seen from another projectile is a

A ball is projected from the foot of an incline plane of inclination $30°,$ at an angle $60°$ with the horizontal with velocity $20\sqrt{3} \mathrm{m} {\mathrm{s}}^{-1}.$ The time after which the ball will strike the plane is

A ball rolls off the top of a stair way with a horizontal velocity $10\sqrt{10} \mathrm{m} {\mathrm{s}}^{-1}.$ If the steps are $0.25 \mathrm{m}$ high and $5 \mathrm{m}$ wide then the ball will hit the edge of the $n^{\mathrm{th} }$ step where $n$ is

A body is projected horizontally with a speed $v_0.$ Find the velocity of the body when it covers equal distances in horizontal and vertical directions.

A stone is thrown from the top of a tower at an angle of $30°$ above the horizontal level with a velocity of $40 \mathrm{m} {\mathrm{s}}^{-1}.$ It strikes the ground after $5$ second from the time of projection then the height of the tower is

A grasshopper can jump a maximum horizontal distance of $40 \mathrm{cm}.$ If it spends negligible time on the ground then in this case its speed along the horizontal road will be

When two projectiles are fired from complementary angles having times of flight $T_1,T_2$ and maximum heights ${\mathrm{H}}_1,{\mathrm{H}}_2$ respectively, which of the following is incorrect?

A projectile is fired to have maximum range $500 \mathrm{m}.$ Maximum height attained by the projectile in this case will be

A projectile is thrown with an initial velocity $\left(v_x\hat{\mathrm{i}}+v_y\hat{\mathrm{j}}\right) \mathrm{m} {\mathrm{s}}^{-1}.$ If the range of the projectile is double the maximum height, then $\frac{v_y}{v_x}$ is

In projectile motion, why we resolve the velocity in two mutually perpendicular direction?

One second after projection, a stone moves at an angle of $45°$ with the horizontal. Two seconds after projection, it moves horizontally. Its angle of projection is (in degrees) $\left(g=10 \mathrm{m} {\mathrm{s}}^{-2}\right)$

If the horizontal range of projectile be a and the maximum height attained by it is $b,$ then velocity of projection is

The speed of a projectile when it is at its maximum height is $\sqrt{\frac{2}{5}}$ times its speed at half the maximum height. What is its angle of projection?