Question

Two projectile launchers are beside one another on level ground. Both launchers are directed at the same angle with respect to ground. Projectile A is launched with an initial speed v, and projectile Bis launched with an initial speed 2v. How do the ranges of the two projectiles compare with one another? (a) Projectile B will travel 4 times as far as projectile A prior to landing (b) Projectile B will travel 3 times as far as projectile A prior to landing (c) Projectile B will travel twice as far as projectile A prior to landing (d) Projectile B will travel 2.5 times as far as projectile A prior to landing

Answer 1

Answer:

(a) Projectile B will travel 4 times as far as projectile A prior to landing

Explanation:

Initial velocity = v

Angle at which the projectile is shot at = θ

g = Acceleration due to gravity

Range of a projectile is given by

$R=\frac {v^{2}\sin 2\theta}{g}$

When Initial velocity = v

$R_A=\frac{v^{2}\sin 2\theta}{g}$

When Initial velocity = 2v

$R_B=\frac{(2v)^{2}\sin 2\theta}{g}\\\Rightarrow R_B=\frac{4v^2\sin 2\theta}{g}$

Dividing the equtions, we get

$\frac{R_A}{R_B}=\frac{\frac{v^{2}\sin 2\theta}{g}}{\frac{4v^2\sin 2\theta}{g}}$

Here, the angle at which the projectiles are fired at are equal.

$\frac{R_A}{R_B}=\frac{1}{4}\\\Rightarrow R_B=4R_A$

Hence, projectile B will travel 4 times as far as projectile A prior to landing