Question

on a planet ,if R is the horizontal range and h,the greatest height of a projectile then it's initial speed is(g on a planet is 32 m/s^2​

Answer 1

Given : on a planet, if R is the horizontal range and h, the greatest height of a projectile. acceleration due to gravity on the planet is 32 m/s².

To find : initial speed of the planet.

solution : let u is the initial speed and θ is the angle of projection.

now horizontal range , R = u²sin2θ/a

⇒R = u²(2sinθcosθ)/a ........(1)

, where a is acceleration due to gravity on that planet.

maximum height, H = u²sin²θ/2a ......(2)

from equations (1) and (2) we get,

R/H = 4/tanθ

⇒tanθ = 4H/R

sinθ = 4H/√{16H² + R²}

Now H = u²sin²θ/2a

⇒H = u²[4H/√(16H² + R²)]²/2 × 32

⇒H = u² [ 16H²/(16H² + R²)/64

⇒64H = 16H²u²/(16H² + R²)

⇒4(16H² + R²) = Hu²

⇒2√(16H² + R²)/√H = u

⇒u = 2√{(16 H² + R²)/H}

Therefore the initial speed of projectile is 2√{(16H² + R²)/H}