Physics Circle home Student Login

Home›Chapters›Projectile Motion PYQs›Relative Velocity in Two Dimensions›Question 24

JEE Main 2013 (25 Apr, Shift 1) · Relative Velocity in Two Dimensions

Relative Velocity in Two Dimensions question from JEE Main 2013 (25 Apr, Shift 1)

Q24JEE Main 2013 · 25 APR · SHIFT 1Difficult

Relative Velocity in Two Dimensions

The maximum range of a bullet fired from a toy pistol mounted on a car at rest is R0=40R_0 = 40 m. What will be the acute angle of inclination of the pistol for maximum range when the car is moving in the direction of firing with uniform velocity v=20v = 20 m/s on a horizontal surface? (g=10g = 10 m/s2^{2})

Show answer and solution

Answer: (b)

  1. At rest: R0=u2g=40⇒u=20R_0 = \dfrac{u^2}{g} = 40 \Rightarrow u = 20 m/s.
  2. Car moving: horizontal speed ucos⁡θ+vu\cos\theta + v, flight time 2usin⁡θg\dfrac{2u\sin\theta}{g}, so R=2usin⁡θg(ucos⁡θ+v)R = \dfrac{2u\sin\theta}{g}(u\cos\theta + v).
  3. dRdθ=0⇒ucos⁡2θ+vcos⁡θ=0⇒20(2cos⁡2θ−1)+20cos⁡θ=0\dfrac{dR}{d\theta} = 0 \Rightarrow u\cos 2\theta + v\cos\theta = 0 \Rightarrow 20(2\cos^2\theta - 1) + 20\cos\theta = 0
  4. 2cos⁡2θ+cos⁡θ−1=0⇒cos⁡θ=122\cos^2\theta + \cos\theta - 1 = 0 \Rightarrow \cos\theta = \dfrac{1}{2}
  5. So the answer is (b) 60∘60^\circ.
Report a mistake

More questions on Relative Velocity in Two Dimensions