Projectile Motion Question: Football Kicker's Goal Post Dilemma

[Strik3r]

Homework Statement

Well to sum up the question: a football kicker kicks a ball with 20m/s initial velocity with a 53 degree angle. the goal post is 36m away and is 3.05m tall. does the ball pass the goal post? does the ball approach the crossbar while still rising or falling?

range=36m
acceleration= -9.8 m/s/s
V initial = 20m/s
angle theta= 53 degrees
height of post=3.05m

Homework Equations

range= (velocity initial x) multiply (time)
vix (velocity initial x) = vi cos angle theta
viy (velocity initial y) = vi sin angle theta

y=(viy) multiply (time) + 0.5at^2

The Attempt at a Solution

using the above information i found the that the ball crosses the goal post by 0.85meters.

here the problem. i don't know how to do the second part. any and all help will be appreciated thx.

 

[hage567]

You could find out at what range the maximum height occurs. Is this before or after the goal post?

 

[baba89]

Based on the given information, it is possible to determine that the ball will indeed pass the goal post, with a horizontal distance of 0.85 meters remaining before reaching the post. This can be calculated using the equations for projectile motion, as you have correctly done.

To determine if the ball will approach the crossbar while rising or falling, we can look at the vertical component of its velocity. Since the initial velocity is 20 m/s at an angle of 53 degrees, we can find the vertical component using the formula viy = vi sin theta. In this case, viy = 20 sin 53 = 16.18 m/s.

Next, we can use the equation y = viy t + 0.5at^2 to determine the height of the ball at any given time. Since we are interested in the height of the ball when it reaches the goal post, we can set y = 3.05 m and solve for t. This gives us t = 0.63 seconds.

Now, we can look at the vertical component of the ball's velocity at this time. Using the formula vf = vi + at, we can find that the vertical velocity at t = 0.63 seconds is 16.18 - 9.8(0.63) = 10.17 m/s. This means that the ball is still rising when it reaches the goal post.

In conclusion, the ball will pass the goal post with 0.85 meters remaining before reaching it, and it will be rising when it does so. I hope this helps clarify the second part of the problem. Let me know if you have any further questions.