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

In summary, the conversation discusses the calculation of how much a kicked football clears or falls short of clearing a crossbar at a certain distance and height, as well as the direction of the ball's movement while approaching the crossbar. The relevant equations used are for horizontal and vertical velocities, displacement, and gravity. The need for a negative sign in one of the equations is explained in terms of the direction of velocity and acceleration.
  • #1
Mindstein
14
0

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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  • #2
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.
 
  • #3
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!
 

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

The negative sign in the formula represents the direction of the displacement. In this case, it indicates that the displacement is in the downward direction.

2. What does the negative sign in the formula mean?

The negative sign indicates that the displacement is in the opposite direction of gravity, which is downwards.

3. Is the negative sign necessary in the formula?

Yes, the negative sign is necessary in the formula to accurately represent the direction of the displacement in relation to gravity.

4. Can the negative sign be ignored in the formula?

No, the negative sign should not be ignored as it plays a crucial role in determining the direction of the displacement and therefore affects the accuracy of the calculation.

5. Why is the displacement considered negative when the object is moving upwards?

If the object is moving upwards, the displacement is still considered negative because it is in the opposite direction of gravity. In this case, the displacement is in the upward direction, while gravity is acting downwards.

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