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JEE Main 2024 (8 Apr, Shift 2) · Horizontal Projectile & Inclined Plane

Horizontal Projectile & Inclined Plane question from JEE Main 2024 (8 Apr, Shift 2)

Q2JEE Main 2024 · 8 APR · SHIFT 2Medium

Horizontal Projectile & Inclined Plane

A body of mass M thrown horizontally with velocity v from the top of the tower of height H touches the ground at a distance of $100\text{ m}$ from the foot of the tower. A body of mass $2M$ thrown at a velocity $\frac{v}{2}$ from the top of the tower of height $4H$ will touch the ground at a distance of _______ m.

Numerical answer type. Work it out, then open the answer.

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Answer: 100

Horizontal range from a tower: $R = v\sqrt{\frac{2H}{g}}$ (independent of mass).
New: $R' = \frac{v}{2}\sqrt{\frac{2(4H)}{g}} = \frac{v}{2} \cdot 2\sqrt{\frac{2H}{g}} = R$
$R' = 100\text{ m}$

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