Projectile Motion

For a body projected at an angle with the horizontal from the ground, choose the correct statement

Two bodies are projected from ground with same speeds $40 \mathrm{m} {\mathrm{s}}^{-1}$ at two different angles with respect to horizontal. The bodies were found to have same range. If one of the body was projected at an angle of $60°$, with horizontal then sum of the maximum heights, attained by the two projectiles, is _____ $\mathrm{m}$. (Given $g=10 \mathrm{m} {\mathrm{s}}^{-2}$)

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

The initial speed of a projectile fired from ground is $u$. At the highest point during its motion, the speed of projectile is $\frac{\sqrt{3}}{2}u$. The time of flight of the projectile is:

A stone is projected at angle $30°$ to the horizontal. The ratio of kinetic energy of the stone at point of projection to its kinetic energy at the highest point of flight will be :

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

The maximum vertical height to which a man can throw a ball is $136 \mathrm{m}$. The maximum horizontal distance upto which he can throw the same ball is

A ball is projected with kinetic energy $E$, at an angle of $60°$ to the horizontal. The kinetic energy of this ball at the highest point of its flight will become :

An object is projected in the air with initial velocity $u$ at an angle $\theta$. The projectile motion is such that the horizontal range $R$, is maximum. Another object is projected in the air with a horizontal range half of the range of first object. The initial velocity remains same in both the case. The value of the angle of projection, at which the second object is projected, will be _____  degree.

A body of mass $10 \mathrm{kg}$ is projected at an angle of $45°$ with the horizontal. The trajectory of the body is observed to pass through a point $\left(20,10\right)$. If $T$ is the time of flight, then its momentum vector, at time $t=\frac{T}{\sqrt{2}}$, is _____ .
[Take $g=10 \mathrm{m} {\mathrm{s}}^{-2}$]

A ball of mass $m$ is thrown vertically upward. Another ball of mass $2 \mathrm{m}$ is thrown an angle $\theta$ with the vertical. Both the balls stay in air for the same period of time. The ratio of the heights attained by the two balls respectively is $\frac{1}{x}$. The value of $x$ is _____ .

Two projectiles are thrown with same initial velocity making an angle of $45°$ and $30°$ with the horizontal respectively. The ratio of their respective ranges will be

If the initial velocity in horizontal direction of a projectile is unit vector $\hat{i}$ and the equation of trajectory is $y=5x\left(1-x\right)$. The $y$ component vector of the initial velocity is _____  $\hat{j}$

(Take $g=10 \mathrm{m} {\mathrm{s}}^{-2}$)

Two projectile thrown at $30°$ and $45°$ with the horizontal respectively, reach the maximum height in same time. The ratio of their initial velocities is

A ball is projected from the ground with a speed $15{ \mathrm{m} \mathrm{s}}^{-1}$ at an angle $\theta$ with horizontal so that its range and maximum height are equal, then $\tan \theta$ will be equal to

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 $h_1$ and $h_2$ respectively, then $R=4\sqrt{h_1{h}_2}$

Reason R: Product of said heights, $h_1{h}_2=\left(\frac{u^2{\sin }^2\theta }{2g}\right)·\left(\frac{u^2{\cos }^2\theta }{2g}\right)$.

A body is projected from the ground at an angle of $45°$ with the horizontal. Its velocity after $2 \mathrm{s}$ is $20{ \mathrm{m} \mathrm{s}}^{-1}$. The maximum height reached by the body during its motion is _____ $m$. (use $g=10{ \mathrm{m} \mathrm{s}}^{-2}$)

A projectile is projected with velocity of $25 \mathrm{m} {\mathrm{s}}^{-1}$ 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 : [$\mathrm{use} \mathrm{g}=10 \mathrm{m} {\mathrm{s}}^{-2}$]

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

An object is thrown vertically upwards. At its maximum height, which of the following quantity becomes zero ?