Question 47: Motion in 2D & Vectors

Question

Two projectiles A and B are thrown with initial velocities of $$40 \mathrm{~m} / \mathrm{s}$$ and $$60 \mathrm{~m} / \mathrm{s}$$ at angles $$30^{\circ}$$ and $$60^{\circ}$$ with the horizontal respectively. The ratio of their ranges respectively is $$\left(g=10 \mathrm{~m} / \mathrm{s}^{2}\right)$$

Accepted Answer

The range of a projectile launched with an initial velocity $v$ at an angle $	heta$ with respect to the horizontal is given by:
$R = \frac{v^2 \sin(2	heta)}{g}$,
where $g$ is the acceleration due to gravity.
Let's calculate the ranges of projectiles A and B:
For projectile A, $v = 40 \, 	ext{m/s}$ and $	heta = 30^\circ$, so:
$R_A = \frac{(40)^2 \sin(2 	imes 30)}{10} = 4 	imes 40 = 160 \, 	ext{m}$.
For projectile B, $v = 60 \, 	ext{m/s}$ and $	heta = 60^\circ$, so:
$R_B = \frac{(60)^2 \sin(2 	imes 60)}{10} = 6 	imes 60 = 360 \, 	ext{m}$.
Therefore, the ratio of their ranges is $R_A : R_B = 160 : 360 = 4 : 9$.

Answer

$$4: 9$$

Answer

$$2: \sqrt{3}$$

Answer

$$\sqrt{3}: 2$$

Answer

$$1: 1$$

Motion in 2D & Vectors

Two projectiles A and B are thrown with initial velocities of $40 \mathrm{~m} / \mathrm{s} and 60 \mathrm{~m} / \mathrm{s} at angles 30^{\circ} and 60^{\circ} with the horizontal respectively. The ratio of their ranges respectively is \left(g=10 \mathrm{~m} / \mathrm{s}^{2}\right)

Choose the correct answer: