Maximum height of a projectile thrown from a rooftop

AI Thread Summary
A rock is thrown from a rooftop 14.6 meters high with an initial velocity of 30.8 m/s at a 33.2-degree angle. The y-component of the velocity is calculated to be 16.86 m/s, and the time to reach maximum height is determined to be 1.72 seconds. The maximum height above ground is computed as 29.1 meters, but it needs adjustment to reflect the height above the roof. The error was identified as the need to subtract the building's height from the total height. The correct maximum height above the roof is thus clarified.
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Homework Statement



A man stands on the roof of a building of height 14.6m and throws a rock with a velocity of magnitude 30.8m/s at an angle of 33.2∘ above the horizontal. You can ignore air resistance.

Calculate the maximum height above the roof reached by the rock.

Homework Equations



Velocity and position equations

Basic trigonometry

The Attempt at a Solution



Initially, I solved for the y-component of the velocity vector given: V=30.8*Sin(33.2)=16.86m/s

Then, I solved for the amount of time it would take for the rock to reach maximum height, where the velocity of the y-component vector is equal to 0: Vy=Voy+g*t=16.86-9.8t=1.72s

I plug this time into the position equation of Y=Yo+Voy*t+g*t^2=14.6+16.86(1.72)-4.9(1.72)^2=29.1m

So, the maximum height should be equal to 29.1m. Not sure why this is incorrect... Perhaps I calculated the vector incorrectly?
 
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Calculate the maximum height above the roof reached by the rock.
You calculated the maximum height above the ground (and I can confirm this value).
 
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Ah, so I just needed to subtract the height of the roof... Simple detail I missed... Thank you!
 
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