An object is thrown withy a fixed initial speed v0 at various angles a relative to the horizona. at some constant height habove the launch point the speed v of the objecet is mraesured as a function of the initial angle

v = √(v²₀Sin² Ф -2ghₐ)

Explanation:

According to the Law of vertical motion  under gravity:

V² = U² ± 2gH (1)

V = final velocity

U = Initial velocity

g = acceleration due to gravity

H = Height of object

According to the  question,

V = v

U = v₀

H = hₐ

Substituting  into  (1)

v² =  v₀² - 2ghₐ (2)

The minus sign was used in the question because  the object motion is against gravity.

Since the object was projected at an angle Ф to the horizontal, the vertical component of the initial velocity is given as :

v₀Sin Ф

Substituting into  equation (2) we have:

v² =  v²₀Sin² Ф -2ghₐ

v = √(v²₀Sin² Ф -2ghₐ) (3)

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