Question

A projectile fired with initial velocity at some angle , has a range R. If
the initial velocity be doubled at: the same angle of projection, then the

range will be

A. R/2

B. R

C. 2R

D. 4R​

Answer 1

Solution :

⏭ Given:

✏ A projectile is fired with initial velocity u at some angle, has a range R.

⏭ To Find:

✏ What will be the range, if initial velocity of projection be doubled at the same angle of projection.

⏭ Formula:

✏ Formula of range in projectile motion is given by

$\bigstar \: \underline{ \boxed{ \bold{ \sf{ \pink{R = \dfrac{ {u}^{2} \sin2 \theta}{g}}}}}} \: \bigstar$

⏭ Terms indication:

• R denotes range
• u denotes initial velocity
• $\theta$ denotes angle of prijection
• g denotes gravitational acceleration

⏭ Calculation:

✏ Since, angle of projection and gravitational acceleration are constant, we can say that

$\implies \sf \: \large{ \underline{ \blue{R \propto {u}^{2} }}} \\ \\ \implies \sf \: \dfrac{R}{R'} = \dfrac{ {u}^{2} }{ {u'}^{2} } \\ \\ \implies \sf \: \dfrac{R}{R'} = \dfrac{ \cancel{{u}^{2}} }{4 \: \cancel{ {u}^{2}} } \: \: ( \because \: u' = 2u) \\ \\ \implies \: \underline{ \boxed{ \bold{ \sf{ \orange{ \large{R' = 4R}}}}}} \: \gray{ \bigstar}$