Why is the sign in the formula Δy=VoyT - (1/2)at² negative in this problem

AI Thread Summary
The discussion focuses on understanding the negative sign in the equation Δy = VoyT - (1/2)at² for projectile motion. The placekicker's football is analyzed, revealing that the ball clears the crossbar by approximately 0.9 meters. The negative sign accounts for gravity's downward acceleration, which opposes the initial upward velocity. As the ball rises, its vertical velocity decreases until it reaches its peak height, after which it becomes negative during its descent. The importance of direction in velocity and acceleration is emphasized in solving such problems.
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Homework Statement


A placekicker must kick a football from a point 36.0 m (about 40 yards) from the goal, and half the crowd hopes the ball will clear the crossbar, which is 3.05 m high. When kicked, the ball leaves the ground with a speed of 20.0 m/s at an angle of 53.0º to the horizontal.
(a) By how much does the ball clear or fall short of clearing the crossbar?
(b) Does the ball approach the crossbar while still rising or while falling?


Homework Equations


1.)Vox= Vo*CosΘ
2.)Voy= Vo*SinΘ
3.)Δx=x=VoxT where T (caps) is equal to time and not period.(its caps to discern from the sub 'ox')
4.)Δy= VoyT - (1/2)gt²


The Attempt at a Solution



Vxi = 20Cos(53)= 12.07 m/s
Vyi = 20Sin(53)= 15.97 m/s

36.0 m = (12.03 m/s)t → t = 3.00 seconds

Δy= (15.97 m/s)(3.00 seconds) - (1/2)(9.8 m/s²)(9.00 seconds²)
Δy = 3.9 meters
Clears by .9 meters...approximately
(the answer is .889 m while descending)

So, I obviously figured out how to do the problem, but I want to know why Relevant Equation 4.) requires me to use a negative sign instead of a positive one.

May someone shed some light. I am obviously missing something very similiar. I tend to complicate things too much.
 
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The direction of velocity and acceleration matters.

You choose Vy as positive y, then g is going to be negative.

It starts out with Vy and all the time gravity is working to reverse it and return it to earth.

Vy gets smaller until it is 0 at max height, then it becomes negative on its downward plunge.
 
LowlyPion said:
The direction of velocity and acceleration matters.

You choose Vy as positive y, then g is going to be negative.

It starts out with Vy and all the time gravity is working to reverse it and return it to earth.

Vy gets smaller until it is 0 at max height, then it becomes negative on its downward plunge.


I can not thank you enough! Thank you very much!
 
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