Question

Can a goalkeeper at his goal kick a soccer ball into the opponent’s goal without the ball touching the ground? The distance will be about 95 m. A goalkeeper can give the ball a speed of 30 m/s.

Answer 1

While theoretically possible under perfect conditions, scoring a goal from 95 meters away with a 30 m/s kick would be highly improbable in an actual soccer match, given real-world factors like air resistance and the necessity of a precise kick angle.

Step-by-step explanation:

Assuming perfect conditions, kicking a soccer ball about 95 meters (the length of a soccer pitch) directly into the opponent's goal without the ball touching the ground could be theoretically possible, but highly improbable in practice. If a goalkeeper can kick the ball with an initial speed of 30 m/s, we can use the physics of projectile motion to determine whether the ball could travel the required distance. The two main factors to consider here are the angle of the kick and the aerodynamic properties of the ball. With no air resistance and at the optimal angle of 45 degrees, projectile motion equations can be applied.

However, in reality, factors like air resistance, wind, spin of the ball, and the technical skill required to hit the ball at the exact needed angle combine to make this scenario highly unlikely during an actual game.

Answer 2

The goalkeeper at his goal cannot kick a soccer ball into the opponent’s goal without the ball touching the ground

Step-by-step explanation:

Consider the vertical motion of ball,

We have equation of motion v = u + at

Initial velocity, u = u sin θ

Final velocity, v = 0 m/s

Acceleration = -g

Substituting

v = u + at

0 = u sin θ - g t

`t=(usin\theta )/(g)`

This is the time of flight.

Consider the horizontal motion of ball,

Initial velocity, u = u cos θ

Acceleration, a =0 m/s²

Time,
`t=(usin\theta )/(g)`

Substituting

s = ut + 0.5 at²

`s=ucos\theta * (usin\theta )/(g)+0.5* 0* ((usin\theta )/(g))^2\\\\s=(u^2sin\theta cos\theta)/(g)\\\\s=(u^2sin2\theta)/(2g)`

This is the range.

In this problem

u = 30 m/s

g = 9.81 m/s²

θ = 45° - For maximum range

Substituting

`s=(30^2* sin(2* 45))/(2* 9.81)=45.87m`

Maximum horizontal distance traveled by ball without touching ground is 45.87 m, which is less than 95 m.

So the goalkeeper at his goal cannot kick a soccer ball into the opponent’s goal without the ball touching the ground