Aplayer kicks a soccer ball from ground level and sends it flying at an angle of 30 degrees at a speed of 26 m/s. what is the maximum height attained by the ball? round the answer to the nearest tenth of a meter

8.6 m

Explanation:

The motion of a soccer ball is a motion of a projectile, with a uniform motion along the horizontal (x-) direction and an accelerated motion along the vertical (y-) direction, with constant acceleration towards the ground (we take upward as positive direction, so acceleration is negative).

The initial velocity along the vertical direction is

Now we can consider the motion along the vertical direction only. the vertical velocity at time t is given by:

At the point of maximum height, , so we can find the time t at which the ball reaches the maximum height:

And now we can use the equation of motion along the y-axis to find the vertical position of the ball at t=1.33 s, which corresponds to the maximum height of the ball:

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