Question

If the range of a projectile be R, then its kinetic energy is
minimum after covering from start a distance equal to:
(a) R/4
(b) R/2
(c) 3R4
(d) R​

Answer 1

Given :

▪ A body is projected from the ground.

▪ Maximum horizontal distance (Range) covered by body = R

To Find :

▪ Distance from initial postion where kinetic energy of body becomes minimum.

SoluTioN :

☞ Since mass of projectile is constant throughout the projectile motion therefore KE of body depends only on the velocity.

☞ Velocity is maximum at the points of projection and landing.

☞ Kinetic energy is maximum at that both points.

☞ Velocity is minimum at the top height of projectile.

☞ Maximum height is achieved at distance half of its maximum ranfe therefore velocity is minimum at a distance of R/2.

☞ Therefore, KE is also minimum at distance R/2.

Option-B ✔

Answer 2

${\bold{\huge{\underline{\pink{\underline{ANSWER:-}}}}}}$

$\boxed{Given}$

• Range of projectile = “R”

✔️we have know that,

• Kinetic energy is minimum where the velocity of projectile is minimum .
• Velocity is minimum at top most point of projectile motion .
• At top most point “the vertical component of velocity is zero” and only horizontal component of velocity is present .
• So, Kinetic energy is minimum at the top most point of the projectile motion .

✔️At the top most point the Range of projectile is half of the total Range of the projectile motion .

☞Hence, It's Kinetic energy is minimum after covering from start a distance equal to “R/2” .

$\bigstar\:\underline{\boxed{\bf{\red{Required Answer}:R/2}}}$