Projectiles are difficult...?

Question

"In 1936, Jesse Owens established a world's running broad jump record of 8.09 m at the Olympic Games at Berlin (where g = 9.8128 m/s2). Assuming the same values of v0 and θ0, by how much would his record (in cm) have differed if he had competed instead in 1956 at Melbourne (where g = 9.7999 m/s2)?"

i have the equation for range which is R = (vo^2/g) sin2(theta) . and since i know each value of g and the range, i should be able to write each equation and compare them, but how?

Answer 1

Simply divide the ranges for the two locations and. the identical terms will cancel out. Then solve for the unknown range.

Let R be the range at Berlin:

R = (v₀²/g) ∙ sin(2∙θ)

and R' the range at Melbourne

R' = (v₀²/g') ∙ sin(2∙θ)

Hence:

R' / R = [ (v₀²/g') ∙ sin(2∙θ) ] / [ (v₀²/g) ∙ sin(2∙θ) ]

<=>

R' / R = (g/g')

=>

R' =  R∙(g/g')

= 8.09m ∙(9.8128m/s² / 9.7999m/s²)

= 8.10065m