Question

Derive the Formula for the range and maximum height achieved by a projectile thrown from the origin with initial velocity u at an angle theeta to the horizontal.

Answer 1

Range of projectile:

Maximum distance which projectile covers in horizontal direction is called as range of projectile.

To calculate the range multiply the horizontal component of velocity with the total time.

R = ux × t

R = uicosθ ×2 Visinθ/g

R = ui^2 sin2θ/g

The range will be maximum if θ = 45 degrees.

Height of projectile:

To determine the height of projectile third equation of motion is used,

2as = Vf^2  - Vi^2  

Final velocity will be zero and initial velocity will be Vi sin θ so,

2(-g)h = -ui^2 sin2θ

h = ui^2 sin2θ/2g

if θ = 900 then  

hmax = ui^2/2g