Question

If T₁ and T₂ are the times of flight for two complementary angles, then the range of projectile R is given by –

• A. R = 4g T₁T₂
• B. R = 2g T₁T₂
• C. R = $\frac{1}{4}$g T₁T₂
• D. R = $\frac{1}{2}$g T₁T₂

Answer 1

Answer: (D)

R = $\frac{1}{2}$g T₁T₂

Answer 2

For complimentary angles range is same

T₁ = $\frac{2u\sin\theta}{g}$ and T₂ =$\frac{2u\sin(90 - \theta)}{g}$

T₁ T₂ =$\frac{4u^{2}\sin\theta\cos\theta}{g^{2}}$

and R =$\frac{2u^{2}\sin\theta\cos\theta}{g}$

$\frac{R}{T_{1}T_{2}}$=$\frac{g}{2}$ ̃ R =$\frac{1}{2}$g T₁T₂