First slide

Projection Under uniform Acceleration

Question

Two particles are projected from the same point with the same speed at different angles θ₁ and θ₂ to the horizontal. If their respective times of flights are T₁ and T₂ and horizontal ranges are same then
a) θ₁+θ₂ = 90⁰ b) T₁ = T₂ tan θ₁ c) T₁ = T₂ tan θ₂ d) T₁ sin θ₂ = T₂ sin θ₁

Difficult

A

a, b, d are correct
B

a, c, d are correct
C

b, c, d are correct
D

a, b, c are correct

Solution

Since ranges are same, θ₁+ θ₂ = 90⁰
Now
$\large \therefore \frac{T_1}{T_2}=tan \theta_1$
$\large Again \frac{T_1}{T_2}=\frac{sin \theta_1}{cos\theta_1}=\frac{sin\theta_1}{cos(90^0-\theta_2)}=\frac{sin\theta_1}{sin\theta_2}$
$\large \therefore T_1 sin\theta_2=T_2sin\theta_1$
Hence option -(1) is correct

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