Answer:
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 [tex]a=g=-9.8 m/s^2[/tex] towards the ground (we take upward as positive direction, so acceleration is negative).
The initial velocity along the vertical direction is
[tex]v_{y0} = v_0 sin \theta = (26 m/s)(sin 30^{\circ})=13 m/s[/tex]
Now we can consider the motion along the vertical direction only. the vertical velocity at time t is given by:
[tex]v_y(t)=v_{y0} +at[/tex]
At the point of maximum height, [tex]v_y(t)=0[/tex], so we can find the time t at which the ball reaches the maximum height:
[tex]0=v_{y0}+at\\t=-\frac{v_{y0}}{a}=-\frac{13 m/s}{-9.8 m/s^2}=1.33 s[/tex]
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:
[tex]y(t)=v_{y0}t + \frac{1}{2}at^2=(13 m/s)(1.33 s)+\frac{1}{2}(-9.8 m/s^2)(1.33 s)^2=8.6 m[/tex]
