(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

A projectile returns to its original height after 4.08 seconds, during which time it travels 76.2 meters horizontally. If air resistance can be neglected, what was the projectile's initial speed?

(Use g = 9.80 .)

2. Relevant equations

3. The attempt at a solution

Hey guys I already solved the problem I just want to get some feedback on whether my breakdown of what I did was correct.

So what I did first was split the problem into its X and Y ( horizontal and vertical components).

76.2m=v_{0}(4.08s)

v_{x}=18.67m/s

Then since the projectile returned to its original height this means that its displacement or change in position will be zero. So I can solve for its initial velocity , by doing the following

0=-.5(9.8)(4.08)^2+v_{0}(4.08)

v_{0}=20m/s

Here is where I get confused I know I have to do the magnitude formula to get the intial speed of 27.4. squaroot ((18.67)^2+(20)^2))

My question is why do I have to do that?

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# Projectile motion and initial speed problem

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