# Projectile Motion Problem: Kicking a soccer ball over a fence

• salqmander
salqmander
Homework Statement
A soccer player is practicing their kick on a field. Initially at rest, an 0.8 kilogram ball is kicked directly toward a fence from a distance 25 meters away, as shown above. The ball's velocity as it leaves the kicker's foot is 19 m/s at an angle of 30 degrees above the horizontal. The top of the fence field is 2.5 meters high. The kicker's foot is in contact with the ball for 0.05 seconds. While in flight, the ball doesn't hit any other object, and air resistance is negligible.

Determine whether the ball will hit the fence. If it will, how high up the fence will it hit? If not, how far above the fence will it reach?
Relevant Equations
d = vt + .5at^2
initial velocity y component is (cos30) * 20.

t = 25m / ((cos30) * 20)m/s = 1.45 seconds

d = vt + .5at^2

v= 20sin30

v= 10 , d= 10(1.45s) + .5(-9.8m/s^s)(1.45s)^2

d=4.2m

4.2-2.5 = +1.7m, so the ball will not hit the fence

Last edited:
Looks good, except you use ##20 m/s## instead of ##19 m/s## given in the question?

topsquark
oh I didn't catch that! i'll fix it, thank you

salqmander said:
initial velocity y component is (cos30) * 20.
Have another go (and I'm not referring to whether it's 19 or 20).

should I use the equation
xf = xi + (vx)i delta t
for time and then
yf = yi + vyi delta t- 1/2g t ^2

haruspex said:
Have another go (and I'm not referring to whether it's 19 or 20).
is this right?

xf = xi + (vx)i delta t, xi=0

t = xf / vxi

t = 25m / 19m/s, t = 1.3 seconds
vyi = vi sin theta, vyi = 9.5m/s

yf = yi + vyi delta t- 1/2g t ^2

= 0m + 9.5m/s(1.5) - 0.5(9.8m/s^2)(1.5)^2

yf = 3.2m

3.2-2.5 = +0.7m

salqmander said:
is this right?

xf = xi + (vx)i delta t, xi=0

t = xf / vxi

t = 25m / 19m/s, t = 1.3 seconds
vyi = vi sin theta, vyi = 9.5m/s

yf = yi + vyi delta t- 1/2g t ^2

= 0m + 9.5m/s(1.5) - 0.5(9.8m/s^2)(1.5)^2

yf = 3.2m

3.2-2.5 = +0.7m
In post #4 I quoted one of your equations. Why am I finding fault with it?

oh its sin not cos

salqmander said:
t = xf / vxi

t = 25m / 19m/s, t = 1.3 seconds
Also, do you see a similar problem above?

kuruman said:
Also, do you see a similar problem above?
yes, i solved for horizontal position not vertical position

salqmander said:
yes, i solved for horizontal position not vertical position
That's not it. You solved for the time of flight. Do you see what's wrong with it?

salqmander said:
Homework Statement: A soccer player is practicing their kick on a field. Initially at rest, an 0.8 kilogram ball is kicked directly toward a fence from a distance 25 meters away, as shown above. The ball's velocity as it leaves the kicker's foot is 19 m/s at an angle of 30 degrees above the horizontal. The top of the fence field is 2.5 meters high. The kicker's foot is in contact with the ball for 0.05 seconds. While in flight, the ball doesn't hit any other object, and air resistance is negligible.

Determine whether the ball will hit the fence. If it will, how high up the fence will it hit? If not, how far above the fence will it reach?
Relevant Equations: d = vt + .5at^2

initial velocity y component is (cos30) * 20.

t = 25m / ((cos30) * 20)m/s = 1.45 seconds

d = vt + .5at^2

v= 20sin30

v= 10 , d= 10(1.45s) + .5(-9.8m/s^s)(1.45s)^2

d=4.2m

4.2-2.5 = +1.7m, so the ball will not hit the fence

This solution was correct, apart from the typo(?) of y component, rather than x component. It was subsequently used as the x-component. And, the use of the wrong initial speed. Subsequent attempts seem to have deteriorated somewhat!

haruspex

## What is projectile motion in the context of kicking a soccer ball?

Projectile motion refers to the motion of an object that is launched into the air and influenced only by gravity and its initial velocity. In the context of kicking a soccer ball, it involves analyzing the ball's trajectory as it is kicked over a fence, taking into account the initial speed, angle of the kick, and the effects of gravity.

## How do you calculate the initial velocity needed to kick a soccer ball over a fence?

To calculate the initial velocity needed, you need to know the height of the fence, the distance from the kicking point to the fence, and the angle at which the ball is kicked. Using the equations of projectile motion, you can solve for the initial velocity by setting up the vertical and horizontal motion equations and ensuring the ball clears the fence.

## What role does the angle of the kick play in projectile motion?

The angle of the kick significantly affects the trajectory of the soccer ball. A higher angle results in a higher but shorter trajectory, while a lower angle results in a longer but flatter trajectory. The optimal angle for maximum range in ideal conditions (no air resistance) is 45 degrees, but this may vary based on the specific requirements of clearing the fence.

## How do you determine the time of flight for the soccer ball?

The time of flight can be determined by analyzing the vertical component of the motion. By using the initial vertical velocity and the acceleration due to gravity, you can calculate the time it takes for the ball to reach its peak height and then return to the ground. The total time of flight is the sum of the time to reach the peak and the time to descend from the peak.

## How can air resistance affect the projectile motion of a soccer ball?

Air resistance can significantly affect the projectile motion by reducing the ball's range and altering its trajectory. It acts opposite to the direction of motion, causing the ball to slow down more quickly than it would in a vacuum. To account for air resistance, more complex models and calculations are required, often involving drag coefficients and numerical methods to solve the equations of motion.

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