Answer;
V = 14.7 m/s
Explanation and solution;
Vx = V cos theta
Vx = 16m/s × cos 28.08
Vx = 14.1 m/s
Vy = Vsin theta
Vy = 7.51m/s
t = d/Vx
t = 16.8m/ 14.1
t= 1.191 s
Now, find Vy at t= 1.191
Vy = Vy - gt
Vy = 7.51 - 9.81*1.191
Vy = - 4.18 m/s
V = sqrt (Vy^2 +Vx^2)
V= sqrt (4.18^2 + 14.1^2)
V= 14.7m/s
The speed of the ball when the goalie catches it in front of the net is 15.97 m/s.
What is Kinematic Equations of Motion?
The mathematical expressions that deal with the various variables like velocity, acceleration, distance, and time period at a given point, is known as the kinematic equation of motion.
Given data -
The distance of the goal is, d = 16.8 m.
The speed of the ball leaving the foot is, v = 16.0 m/s.
The angle of projection is, [tex]\theta = 28.08^{\circ}[/tex].
Calculating the horizontal and vertical component of velocity as,
[tex]v_{x}=v \times cos \theta\\v_{x}=16 \times cos 28.08\\v_{x}=14.1 \;\rm m/s\\\\v_{y} =v \times sin \theta\\v_{y} = 16 \times sin28.08\\v_{y}=7.51 \;\rm m/s[/tex]
Now, the speed of the ball when the goalie catches it in front of the net is ,
[tex]v = \sqrt{v^2_{x}+v^2_{y}}\\\\v = \sqrt{14.1^2+7.51^2}\\\\v=15.97\;\rm m/s[/tex]
Thus, we can conclude that the speed of the ball when the goalie catches it in front of the net is 15.97 m/s.
Learn more about the kinematics of motion here:
https://brainly.com/question/5955789
