Question

Two projectiles u₁ and u₂, with speed of 40 m/s and 60 m/s respectively are thrown at a certain angle, u₁ with 30^o and u₂ with 60^o, what is the ratio of range?

Answer 1

Correct Answer: 49

The correct answer is 4/9

Answer 2

The horizontal range of a projectile depends on its initial speed and the angle at which it is launched. The formula for the range R of a projectile launched at an angle θ with an initial speed u is:
\(R = \frac{u^2 sin(2θ)}{g}\)
where g is the acceleration due to gravity.
For the first projectile, u₁ = 40 \(\frac{m}{s}\) and θ₁ = \(30^{\circ}\). Therefore, the range R₁ of the first projectile is:
\(R_1 = \frac{40\frac{m}{s}^2 sin(2*30^{\circ})}{g}\) = 80 m
For the second projectile, u₂ = 60 \(\frac{m}{s}\) and θ₂ = \(60^{\circ}\). Therefore, the range R₂ of the second projectile is:
\(R_2 = \frac{60\frac{m}{s}^2 sin(2*60^{\circ})}{g}\) = 180 m
The ratio of the ranges is:
\(\frac{R_2}{R_1}\) = \(\frac{180m}{80m}\)= \(\frac{9}{4}\)
Therefore, the ratio of the ranges of the two projectiles is 9:4.
Answer. \(\frac{9}{4}\)