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Two projectiles of same mass and with same velocity are thrown at an angle $60^\circ$ and $30^\circ$ with the horizontal, then which quantity will remain same :
A
Time of flight
B
Horizontal range of projectile
C
Max height acquired
D
All of them
Detailed Solution
Horizontal range: $R = \dfrac{u^2\sin 2\theta}{g} = \dfrac{2u^2\sin\theta\cos\theta}{g}$
For $\theta = 60^\circ$: $\sin 120^\circ = \dfrac{\sqrt{3}}{2}$; for $\theta = 30^\circ$: $\sin 60^\circ = \dfrac{\sqrt{3}}{2}$. The ranges are equal.
In general, the range is the same for angles of projection $\theta$ and $90^\circ - \theta$.
Time of flight ($\dfrac{2u\sin\theta}{g}$) and maximum height ($\dfrac{u^2\sin^2\theta}{2g}$) are larger for $60^\circ$.
So the horizontal range remains the same.
For $\theta = 60^\circ$: $\sin 120^\circ = \dfrac{\sqrt{3}}{2}$; for $\theta = 30^\circ$: $\sin 60^\circ = \dfrac{\sqrt{3}}{2}$. The ranges are equal.
In general, the range is the same for angles of projection $\theta$ and $90^\circ - \theta$.
Time of flight ($\dfrac{2u\sin\theta}{g}$) and maximum height ($\dfrac{u^2\sin^2\theta}{2g}$) are larger for $60^\circ$.
So the horizontal range remains the same.