Answer
14.7 m/s
Work Step by Step
Let's apply equation 3.5a $S=ut$ in the horizontal direction to find the time taken to reach 16.8m horizontal distance.
$\rightarrow S=ut$ ; Let's plug known values into this equation.
$16.8 m=16\space m/s\times cos28^{\circ}\times t$
$t=1.19\space s$
Let's apply equation 3.5a $V=u+at$ in the vertical direction to find the y-component of velocity at 16.8 m horizontal distance.
$\uparrow V=u+at$
$V_{y}=16\space m/s\times sin28^{\circ}+(-9.8\space m/s^{2})\times1.19\space s$
$V_{y}=-4.15\space m/s$
By using the Pythagorean theorem, we can get.
$V=\sqrt {V_{x}^{2}+V_{y}^{2}}=\sqrt {(14.1\space m/s)^{2}+(-4.15\space m/s)^{2}}=14.7\space m/s$
So, the speed of the ball just as it reaches the goalie is = 14.7 m/s
