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← JEE Main 2014 · 9 Apr · Shift 1
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JEE Main 2014 · 9 Apr · Shift 1, Physics question 2

The position of a projectile launched from the origin at t=0t=0 is given by r⃗=(40i^+50j^)\vec r=\left(40\hat i+50\hat j\right) m at t=2t=2 s. If the projectile was launched at an angle θ\theta from the horizontal, then θ\theta is (take g=10g=10 ms−2^{-2}).

Choose one option
Answer and worked solution

Official answer: C

  • Horizontal: 40=ux⋅240=u_x\cdot2, so ux=20u_x=20 m/s.
  • Vertical: 50=2uy−12(10)(4)50=2u_y-\frac12(10)(4), so uy=35u_y=35 m/s.

tan⁡θ=3520=74\tan\theta=\dfrac{35}{20}=\dfrac74, so θ=tan⁡−174\theta=\tan^{-1}\dfrac74.