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.

$h _{1} h _{2}=\left(\frac{u^{2} \sin ^{2} \theta}{2 g }\right) \cdot\left(\frac{u^{2} \cos ^{2} \theta}{2 g }\right)$

Choose the $CORRECT$ answer 

  • [JEE MAIN 2022]
  • A

    Both $A$ and $R$ are true and $R$ is the correct explanation of $A$.

  • B

    Both $A$ and $R$ are true but $R$ is NOT the correct explanation of $A$.

  • C

    A is true but $R$ is false

  • D

    A is false but $R$ is true

Similar Questions

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 $ms ^{-1}$)

  • [AIIMS 2019]

A shell is fired from a fixed artillery gun with an initial speed $u$ such that it hits the target on the ground at a distance $R$ from it. If $t_1$ and $t_2$ are the values of the time taken by it to hit the target in two possible ways, the product $t_1t_2$ is

  • [JEE MAIN 2019]

The maximum height reached by a projectile is $64 \mathrm{~m}$. If the initial velocity is halved, the new maximum height of the projectile is_________.$\mathrm{m}$.

  • [JEE MAIN 2024]

Range of a bullet fired at $45^o$ to horizontal is $980m$. If the bullet is fired at same  angle from a car travelling horizontally at $18\, km/hr$ towards target then range will be  increased by :-

A player kicks a football with an initial speed of $25\, {ms}^{-1}$ at an angle of $45^{\circ}$ from the ground. What are the maximum height and the time taken by the football to reach at the highest point during motion ? (Take g $=10 \,{ms}^{-2}$ )

  • [JEE MAIN 2021]