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.
x = 30 m
= 40 degree
vo = ?
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we know
x = vo cos * t -------------- (1)
and
yf = yi + vyt + 1/2ayt2
assuming that launch height and landing height of ball is same, we have
0 = vyt + 1/2ay2 -------- (2)
from (1)
t = x / vo cos
put this in (2)
0 = vo sin * ( x / vo cos) - 1/2 * g * (x / vo cos)2
0 = xtan - gx2 / 2vo2 cos2
put the values,
0 = 30 * tan 40 - 9.8 * 302 / 2 * vo2 * cos 2 40
30 * tan 40 = 9.8 * 302 / 2 * vo2 * cos 2 40
vo = 17.3 m/s
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