In a soccer game a midfielder kicks the ball from one touchline directly toward the other with a velocity of 14m/s (along the positive x axis ) after the ball travels for 2.5 seconds a stricker makes an acrobatic kick that gives the ball a new velocity in the y direction and after 0.9 seconds as the ball passes the diving goalkeeper and goes into the net if total displacement of the ball is 40.2 at 29.5 above x positive axis with what speed did the stricker kick the ball

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skyluke89 skyluke89 · Answer 1 · 2019-09-24T12:44:08+02:00

Answer:

5.8 m/s

Explanation:

First, we can find the net velocity of the ball. In fact, we know that the total time of travel is

[tex]t=2.5 s + 0.9 s =3.4 s[/tex]

While the total displacement is

d = 40.2 m

So, the net velocity is

[tex]v=\frac{d}{t}=\frac{40.2}{3.4}=11.8 m/s[/tex]

We know that the direction of the velocity is equal to that of the displacement, so

[tex]\theta=29.5^{\circ}[/tex]

above the positive x axis. Therefore, we can find the velocity along the y-axis:

[tex]v_y = v sin \theta = (11.8)(sin 29.5^{\circ})=5.8 m/s[/tex]

And since the initial motion of the ball was only along the x-axis, we can say that this is the speed at which the stricker kicked the ball.