Question

He is believed to be one of the best Free-kik takers Zambia has ever produced in world of soccer. in one of the crucial matches, he had to take a direct free kick 30.0m from the goal post. he kicked the ball in such a way that it left his foot with a velocity of 22.0m/s at angle of 24° from the horizontal, in the direction of the goal post. did he managed to score? ( take the height of the goal post to be 2.5m and assume that the goal keeper had no ` chance` )​

Answer 1

The projectile launch ratios allow finding the result of whether the ball enters the goal is:  

• When the ball reaches the goal position (x = 30m) it is below the crossbar height (y <h) and enters scoring the goal.

Parameters given

• Distance to goal   x = 30 m

• Ball speed     v₀ = 22.0 m / s

• Angle      θ = 24º

• Goal crossbar eight    h = 2.5 m

To find

• Score the goal

Projectile launching is an application of kinematics where there is not acceleration on the x-axis and there is gravity acceleration on the y-axis.

In this case, to score the goal, the ball must be at maximum h = 2.5 m when it is at x = 30m, let's find the time, see attachment for a schema.

The components of the initial velocity are:

        cos 24 = $\frac{v_o_x}{v_o}$  

        sin 24 = $\frac{v_{oy}}{v_o}$

        v₀ₓ = v₀ cos 24

        $v_{oy}$  = v₀ sin 24

on the x axis there is no acceleration.

        x = v₀ₓ t

        t = $\frac{x}{v_o \ cos 24y}$

Let's  calculate

        t = $\frac{30}{22 \ cos24}$  

        t = 1.49 s

Now let's find out at what height for this time

       y = y₀ + $v_{oy}$  t - ½ g t²

In general for free -kik the ball is on the floor y = 0

      y = v₀ sin 24 t - ½ g t²

 

Let's calculate

     y = 22 sin 24 1.49 - ½ 9.8 1.49²

     y = 2.45 m

It indicates that the height of the goal crossbar is 2.5 m, therefore when the ball arrives it is below the height and enters scoring the goal.

Learn more here:  brainly.com/question/10903823