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JEE Main 2004

Exam: JEE Main
Year: 2004
Subject: Physics
Chapter: Motion in Two Dimensions

JEE Main 2004 · Physics · Motion in Two Dimensions

A projectile can have the same range R for two angles of...

A projectile can have the same range

R

for two angles of projection. If

T_1

and

T_2

be the time of flights in the two cases, then the product of the two time of flights is directly proportional to

Options

A $1 / R^2$
B $1 / \mathrm{R}$
C $\mathrm{R}$
D $\mathrm{R}^2$

Correct answer

C. $\mathrm{R}$

Step-by-step solution

Range is same for complimentary angles.

\mathrm{T}_1=\frac{2 \mathrm{u} \sin \theta}{\mathrm{g}}

and

\mathrm{T}_2=\frac{2 \mathrm{u} \sin (90-\theta)}{\mathrm{g}}

and

R=\frac{u^2 \sin 2 \theta}{\mathrm{g}}

\therefore

\mathrm{T}}_{1} \mathrm{~T}

}_{2}=

\frac{2 \mathrm{u} \sin \theta}{\mathrm{g}} \times \frac{2 \mathrm{u} \cos \theta}{\mathrm{g}}=\frac{2 \mathrm{R}}{\mathrm{g}} \text{. }

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