Find 𝜃 when the range r of a projectile is given by r = 1 32 v02 sin(2𝜃). (Enter your answers as a comma-separated list. Round your answers to one decimal place.)

Question

A baseball is hit at an angle of 𝜃 with the horizontal and with an initial velocity of v₀ = 104 feet per second.

An outfielder catches the ball 300 feet from home plate.

Find 𝜃 when the range r of a projectile is given by r = 1 32  v02 sin(2𝜃). (Enter your answers as a comma-separated list. Round your answers to one decimal place.)

𝜃=___ degrees

Answer 1

I'm not sure what r = 1 32 v02 sin(2Θ) means. It could mean r = 1.32 v² sin(2Θ).

But even if that's not it exactly, you'd do the problem the same way.

r = 300 the range (distance) to the outfielder

v = 140 the initial velocity of the ball

Plugging those numbers in, we get 300 = 1.32 x 140² sin(2Θ), which is sin(2Θ) = .0115955...

Then you do the arcsin of both sides, so 2Θ = .664349... in degrees.

Then divide both sides by 2 and get Θ = .3321898... degrees. And round however you want.

BTW, this is not a realistic physics formula. But if the number 1.32 were something less, like around .04, it'd be a more realistic formula.