What's the minimum initial speed to score

In summary, Alex Morgan kicks the ball straight at the goal from 20.0 m away, and it launches off the ground at an 33.3 degree angle. The goalie is busy faking an injury and the ball reaches the goal without touching the ground. Assuming the ball is kicked at an initial speed greater than if it touched ground, the range formula can tell you what the absolute minimum initial speed is so that the ball hits ground as it reaches the goal. However, this speed is going to be greater than if the ball touched ground so the y displacement will be zero.
  • #1
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Homework Statement


Alex Morgan is going to kick a soccer ball into the Canadians goal during the 2015 world cup. Alex kicks the ball straight at the goal from 20.0 m away, and it launches off the ground at an 33.3 degree angle. Assume the goalie is busy faking an injury and ignore air resistance
a) what's the minimum initial speed that the soccer ball must have to reach the goal without touching the ground?
b)Assume Alex kicks the ball at the speed found in part a). if the Canadian goalie takes 5.00 sec to get back into position to be able to stop the ball, does Alex score the goal?
c) the top of the net is 2.44 m off the ground, what is the maximum initial speed that the soccer ball can have (when the ball leaves her foot at this angle) and not miss scoring?

Homework Equations


5Kb7Y.png

q8L8m.png


The Attempt at a Solution


a) so for the x displacement.
20=0+(vicosθ)t, so t= 20/(vicosθ)
for the y displacement do i not have to calculate it because it's going to be 0? i was not given the y value until part c) so now i don't know where to go about solving for the y displacement.

Are these the correct formulas to be looking at to try and solve this problem?
 
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  • #2
Charlene said:

Homework Statement


Alex Morgan is going to kick a soccer ball into the Canadians goal during the 2015 world cup. Alex kicks the ball straight at the goal from 20.0 m away, and it launches off the ground at an 33.3 degree angle. Assume the goalie is busy faking an injury and ignore air resistance
a) what's the minimum initial speed that the soccer ball must have to reach the goal without touching the ground?
b)Assume Alex kicks the ball at the speed found in part a). if the Canadian goalie takes 5.00 sec to get back into position to be able to stop the ball, does Alex score the goal?
c) the top of the net is 2.44 m off the ground, what is the maximum initial speed that the soccer ball can have (when the ball leaves her foot at this angle) and not miss scoring?

Homework Equations


5Kb7Y.png

q8L8m.png


The Attempt at a Solution


a) so for the x displacement.
20=0+(vicosθ)t, so t= 20/(vicosθ)
for the y displacement do i not have to calculate it because it's going to be 0? i was not given the y value until part c) so now i don't know where to go about solving for the y displacement.
If the ball is kicked at an angle of 33.3 degrees to the horizontal, how can the y displacement be zero?
Are these the correct formulas to be looking at to try and solve this problem?
You have the correct formulas, you just need to apply them correctly to solve this problem.

As an aid to solution, draw a sketch of how the ball travels after being kicked until it reaches the goal.
 
  • #3
okay, so i found
range_equation_initial_velocity.png
but it says this can only be used when the initial and end elevation is the same, which in my problem this isn't going to be true because the end elevation is still in the air when it started on the ground.

so, relooking at the equations,
i have t= 20/(vicosθ)
and for the y,
0=(visinθ)t-1/2gt^2
(not too sure how to solve for t right this second)
then once they are both t= would i set the two equations = to each other and then solve for vi?
 
  • #4
Charlene said:
okay, so i found
range_equation_initial_velocity.png
but it says this can only be used when the initial and end elevation is the same, which in my problem this isn't going to be true because the end elevation is still in the air when it started on the ground.

so, relooking at the equations,
i have t= 20/(vicosθ)
and for the y,
0=(visinθ)t-1/2gt^2
(not too sure how to solve for t right this second)
then once they are both t= would i set the two equations = to each other and then solve for vi?

In a), the problem asks for the minimum initial speed so that the kicked ball reaches the goal without touching the ground. Obviously, this initial speed is going to be greater than if the ball touches ground as it reaches the goal. The range formula can tell you what the absolute minimum initial speed is so that the ball hits ground as it reaches the goal.

In your equations above, there are several quantities which are fixed for this problem, like g and the angle θ.
 
  • #5
I asked one of my classmates for help on this problem and this is the solution he came up with. Isnt this incorrect tho because the range formula isn't keeping in mind that its not hitting the ground? I am honestly so lost and have an exam in a couple hours, hope to figure this out soon!

okay, the picture won't upload but he did the R= (vi^2sin2(theta))/g and solved to get vi=√20g/sin(66.6)=14.6

time to get there then is

b) 20m/(14.6)cos(33.3) = 1.64

c) vi= √ (g xf^2)/ (2cos^2(theta)(tan(theta)xf-yf)
 
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  • #6
Charlene said:
I asked one of my classmates for help on this problem and this is the solution he came up with. Isnt this incorrect tho because the range formula isn't keeping in mind that its not hitting the ground? I am honestly so lost and have an exam in a couple hours, hope to figure this out soon!

http://IMG_20160601_231736 [Broken]

Your classmate's solution didn't post correctly.
 
Last edited by a moderator:
  • #7
SteamKing said:
Your classmate's solution didn't post correctly.
sorry I'm editing it now!
 
Last edited:

What's the minimum initial speed to score?

The minimum initial speed to score varies depending on the specific sport or activity. For example, in basketball, the minimum initial speed to score a basket would be enough momentum to shoot the ball into the hoop. In soccer, the minimum initial speed to score a goal would be enough force to kick the ball past the goalkeeper and into the net.

Can the minimum initial speed to score be determined mathematically?

Yes, the minimum initial speed to score can be calculated using physics principles such as velocity, acceleration, and angle of release. This can be especially useful in sports like golf or tennis where precision and technique are crucial for scoring.

Does the minimum initial speed to score depend on the distance or size of the target?

Yes, the minimum initial speed to score can be affected by the distance or size of the target. In sports like baseball, the minimum initial speed needed to hit a home run may be different depending on the distance to the outfield wall. In bowling, the minimum initial speed required to knock down all the pins may vary depending on the size and weight of the ball.

Is the minimum initial speed to score the same for everyone?

No, the minimum initial speed to score can vary for each individual based on factors such as strength, skill, and technique. For example, a professional athlete may be able to score with a lower initial speed compared to an amateur due to their training and experience.

Can the minimum initial speed to score be improved upon?

Yes, the minimum initial speed to score can be improved through practice, training, and proper technique. By increasing speed, accuracy, and precision, athletes can improve their chances of scoring in various sports and activities.

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