Horizontal range of a projectile

AI Thread Summary
The discussion revolves around calculating the horizontal range of a projectile, specifically a ball tossed from a building with an initial velocity of 7.80 m/s at a 15.0° angle below the horizontal. The user initially calculates the horizontal velocity using the sine function, resulting in an incorrect horizontal distance of 12.11 meters. The correct approach requires using the cosine function for horizontal velocity, leading to the expected distance of 45.2 meters. The confusion stems from misapplying trigonometric functions in the context of projectile motion. Understanding the distinction between vertical and horizontal components is crucial for accurate calculations.
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Homework Statement



A ball is tossed from an upper-story window of a building. The ball is given an initial velocity of 7.80 m/s at an angle of 15.0° below the horizontal. It strikes the ground 6.00 s later.
(a) How far horizontally from the base of the building does the ball strike the ground?


Homework Equations



Vx = xsinTheta

DeltaX = Vx . t

The Attempt at a Solution



Vx = 7.8sin(15) = 2.02 m/s^-1

DeltaX = (2.02)(6) = 12.11m

Something is seriously wrong in my answer although I can't see what. The answer should be 45.2m.
 
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I realize I am using Vx = xsinTheta instead of Vx = xcosTheta, although why is it that? When drawing a triangle of this and doing the trig, I get the first equation, could someone please explain this.
 

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