A projectile is projected with kinetic energy K . If it has maximum possible horizontal range, then

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3-2.Motion in Plane

medium

A projectile is projected with kinetic energy $K$. If it has the maximum possible horizontal range, then its kinetic energy at the highest point will be ......... $K$

$0.25$

$0.5$

$0.75$

$1.0$

Solution

since, range is maximum, therefore $\theta=45^{\circ}$

Hence, $v_{x}=v \cos 45^{\circ}=v / \sqrt{2} .$ At the highest

point, the net velocity of the projectile is

$v_{x}=v \cos 45^{\circ}$

$\therefore \quad \mathrm{KE}=\frac{1}{2} \mathrm{mv}_{\mathrm{x}}^{2}=\frac{1}{2} \mathrm{m} \frac{\mathrm{v}^{2}}{2}=\frac{\mathrm{K}}{2}=0.5 \mathrm{K}$

Standard 11

Physics

A particle is projected at angle $\theta$ with horizontal from ground. The slop $(m)$ of the trajectory of the particle varies with time $(t)$ as ………..

medium

A cricketer can throw a ball to a maximum horizontal distance of $100\, m .$ The speed with which he throws the ball is (to the nearest integer) (in $ms ^{-1}$)

medium

(AIIMS-2019)

In the motion of a projectile freely under gravity, its

easy

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 :

medium

(JEE MAIN-2023)

A stone is projected from ground at $t = 0$. At the time of projection horizontal and vertical component of velocity are $10\, m/s$ and $20\, m/s$ respectively. Then time at which tangential and normal acceleration magnitude will be equal $(g = 10\, m/s^2)$ [neglect air friction] ……… $\sec$

hard

A projectile is projected with kinetic energy $K$. If it has the maximum possible horizontal range, then its kinetic energy at the highest point will be ......... $K$

Solution

Similar Questions

A particle is projected at angle $\theta$ with horizontal from ground. The slop $(m)$ of the trajectory of the particle varies with time $(t)$ as ………..

A cricketer can throw a ball to a maximum horizontal distance of $100\, m .$ The speed with which he throws the ball is (to the nearest integer) (in $ms ^{-1}$)

In the motion of a projectile freely under gravity, its

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