Question

A projectile can have the same range R for two angles of projection. If t₁ and t₂ be the times of flight in two cases, then what is the product of two times of flight?

Options

• t₁t₂ ∝ R

• t₁t₂ ∝ R²

• t₁t₂ ∝ 1/R

• t₁t₂ ∝ 1/R²

Answer 1

t₁t₂ ∝ R

Explanation:

t₁ = `(2"u" sin θ)/"g"` and

t₂ = `(2"u" sin (90 - θ))/"g" = (2"u" cos θ)/"g"`

∴ t₁t₂ = `(4"u"^2 cos θ sin θ)/"g"^2`

= `2/"g" [("u"^2 sin 2θ)/"g"]`

= `2/"g" "R"`

where R is the range.

Hence t₁t₂ ∝ R