Question

The horizontal distance x traveled by a soccer ball if it is kicked from ground level with an initial velocity of v at angle theta is x=1/32(vsquared) sin2theta. Which of the following is an equivalent expression for x?

a. 1/16(vsquared) sintheta
b.1/32(vsquared) cos2theta
c.1/32(vsquared) sinthetacostheta
d.1/16(vsquared) sinthetacostheta

Answer 1

d. 1/16v²sin(θ)cos(θ)

Explanation:

The relevant trig identity is ...

sin(2θ) = 2sin(θ)cos(θ)

Substituting this into the given expression gives ...

x = 1/32v²sin(2θ) = (1/32v²)(2v²sin(θ)cos(θ))

x = 1/16v²sin(θ)cos(θ)