Question

The maximum range of a projectile is 100 km. Take g = 10 ms. The initial velocity of the projectile will be:
(A) 1000 km/s (B)1 km/s 2 (C) 10 km/s (D) 100 km/s
what is answer from these options?​

Answer 1

Range

Define as the horizontal distance which is covered during the projectile motion.

• $\bf R = \dfrac{U^2sin(2\theta)}{g}$
• where R is range, U = initial velocity, $\theta$ = angle by which object is projected.

For range to be maximum:

$\therefore \rm sin( 2\theta)= maximum = 1$

$\implies \rm 2\theta = 90\degree$

$\implies \bf \theta = 45\degree$

Solution:

$\implies \rm maximum \: range =\dfrac{U^2}{g}$

$\implies \rm 100\times 10^3=\dfrac{U^2}{10}$

$\implies \rm U^2 = 10^3\times 10^3$

$\implies \rm U = 1000\: ms^{-1} = \dfrac{1000}{1000}\: kms^{-1}$

$\implies \bf U = 1 \: kms^{-1}$

★ The initial velocity of the projectile is 1 km/s.