Max Range Lab: Solving the Units Problem

[haxtor21]

Homework Statement

I am doing a lab report where I have to find a maximum range and at what angle it occurs. For the range equation I am using a range equation with the initial velocity, theta, g and h as variables. There clearly is a problem since my units do not match up, and I can't find what it is. h has to be zero since the projectile was shot at h=0. Eliminating h still doesn't solve the units problem, but the answer does conform more with my data, but still is 20% off.

Homework Equations

V0=4 m/s
theta=45 deg.

The Attempt at a Solution

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[Redbelly98]

When you bring the term V₀ cosθ inside the radical, and it becomes V₀² cos²θ, the first term in the radical should be

V₀² cos²θ * V₀² sin²θ
= V₀⁴ sin²θ cos²θ​

and then the units agree. (And transform to sin²2θ as appropriate, of course.)

This will make your calculated R larger.