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JEE Main 202225 JulyEvening Shift
Exam
JEE Main
Year
2022
Date
25 July
Shift
Evening Shift
Subject
Physics
Chapter
Motion in Two Dimensions

JEE Main 2022 · 25 July · Evening Shift · Physics · Motion in Two Dimensions

A ball is projected from the ground with a speed 15 ms ^ - 1 at an...

A ball is projected from the ground with a speed 15ms−115{ms}^{- 1} at an angle θ\theta with horizontal so that its range and maximum height are equal, then tanθtan\theta will be equal to

Options

  1. A14\dfrac{1}{4}
  2. B12\dfrac{1}{2}
  3. C22
  4. D44

Correct answer

D. 44

Step-by-step solution

The range and the maximum height of the projectile are given as below,

R=u2sin⁡2θg=2u2sinθcosθgH=u2sin⁡2θ2gR = \dfrac{{u}^{2}\sin 2\theta}{g} = \dfrac{2{u}^{2}sin\theta cos\theta}{g}H = \dfrac{{u}^{2}\sin^{2}\theta}{2g}

Therefore,

As H=RH = R

⇒tanθ=4⇒ tan\theta = 4

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