Question

The ratio of maximum height reached to maximum horizontal range of a projectile depends upon
a) sin α
b) Cos α
c) sin2 α
d) cos2α

Answer 1

ratio of max height to horizontal range is

depends upon sin2alpha

as it is in denominator in 1st step

Answer 2

Concept:

• Projectile motion
• The maximum height of a projectile
• The maximum horizontal range of a projectile

Given:

• The maximum height of a projectile H = u^2sin^2 θ/2g
• The maximum horizontal range of a projectile R = u^2 sin 2θ/g

Find:

• The ratio of maximum height to the maximum horizontal range of a projectile

Solution:

H/R = (u^2sin^2 θ/2g) / (u^2 sin 2θ/g)

H/R = (sin^2 θ/2g) / (sin 2θ/g)

H/R =  (sin^2 θ/2) / (sin 2θ)

H/R =  (sin^2 θ) / (2 sin 2θ)

H/R = sin^2 θ/ 2 (2 sinθ cos θ)

H/R = sin θ/4 cos θ

The correct option is both a and b.

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