Question

A soccer player, centered with the facing the goal net on a field head-on, needs to kick a soccer ball towards the net from 30 meters away. If the ball is kicked at an incline of 40 degrees from the horizontal (ground), what initial speed in m/s must the soccer player give the ball to score without bouncing before the post? Assume no air resistance.

Report the value as an integer.

Answer 1

x = 30 m

$\theta$ = 40 degree

v_o = ?

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we know

x = v_o cos $\theta$ * t -------------- (1)

and

y_f = y_i + v_yt + 1/2a_yt²

assuming that launch height and landing height of ball is same, we have

0 = v_yt + 1/2a_y² -------- (2)

from (1)

t = x / v_o cos$\theta$

put this in (2)

0 = v_o sin $\theta$ * ( x / v_o cos$\theta$) - 1/2 * g * (x / v_o cos$\theta$)²

0 = xtan$\theta$ - gx² / 2v_o² cos²$\theta$

put the values,

0 = 30 * tan 40 - 9.8 * 30² / 2 * v_o² * cos ² 40

30 * tan 40 = 9.8 * 30² / 2 * v_o² * cos ² 40

v_o = 17.3 m/s