Trajectory of two particles projected from origin with speed v1 and v2 and angle θ1 and θ2 with positive x-axis respectively as shown in the figure. Given that \overset{\rightarrow}{g} = - 10 m / s^{2} \left(\right. \textrm{ } \hat{j} \textrm{ } \left.\right). Choose the correct option related to diagram.

Engineering

Physics

Projectile Motion

Question

Trajectory of two particles projected from origin with speed v₁ and v₂ and angle θ₁ and θ₂ with positive x-axis respectively as shown in the figure. Given that $\vec{g} = - 10 m / s^{2} (\hat{j})$ . Choose the correct option related to diagram.

v₁ – v₂ = 2v₁

3(v₁ – v₂) = 2v₁

θ₂ – θ₁ = 2θ₁

3(θ₂ – θ₁) = θ₁

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$10 = \frac{v_{1}^{2} \sin^{2} θ_{1}}{2 g}$ ... (i)
$40 = \frac{v_{1}^{2} \sin^{2} 2 θ_{1}}{g}$ ... (ii)
from (i) and (ii)
$\frac{1}{4} = \frac{\sin θ_{1}}{4 \cos θ_{1}} = \frac{\tan θ_{1}}{4}, θ_{1} = 45 °$
$10 \frac{v_{1}^{2} (1 / 2)}{2 \times 10}$
v₁ = 20 m/s
similarly for second particle
θ₂ = 60° and v₂ = 20 m/s

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