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

A hammer slides off the roof of a house that slopes downward at 40 degrees. The edge of teh roof is 14m avove the ground and the hammer leaves the roof at 7m/s.

How far from the edge of the roof does the hammer strike the ground?

2. Relevant equations

x direction

Vx=V0x

x=V0cosθ

y direction

Vy=V0y−gt

y=V0yt−12gt2

Vy^2=V0y^2−2gy

3. The attempt at a solution

just looking for a quick bit of help here. You can see some of the work I've done in the attached image.

My initial thought was to first decompose the initial velocity vector into its components so I could go ahead and use those in my calculations, which I did, and they seem to check out when compared with the original problems statement on velocity.

Since I'm trying to find the horizontal distance from the roof ledge, I assumed that using this would be the best bet.

[tex](x-x_0)=V_0\cos{\theta}(t)[/tex]

noticing that I need time for this, I decided to use the formula to solve for t

[tex]y={V_{0y}}^2t+\frac{at^2}{2}[/tex]

Where I would let y be -14, since my displacement will be from 14m above 0m (0-14)

however, as you'll see from my work found in the attachment, it looks like I'll keep ending up with complex numbers for time.

I'm wondering whether my assumed initial variables are wrong, or if I've once again made a mathematical blunder?

Any help would be great.

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# Projectile Motion - hammer sliding off a roof

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