Assertion $(A)$: The range of a projectile is maximum when the angle of projection is $45^{\circ}$.
Reason $(R)$: The range of a projectile depends only on the angle of projection.

  • 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.

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$A$ projectile is given an initial velocity of $(3 \hat{i} + 4 \hat{j}) \text{ m s}^{-1}$, where $\hat{i}$ is along the ground and $\hat{j}$ is along the vertical. Assuming $g = 10 \text{ m s}^{-2}$, if the equation of its trajectory can be written as $\frac{1}{9} [\beta x + \gamma x^2]$, then the value of $\gamma$ is

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