Can you solve this difficult physics problem?

Question

A soccer player kicks the ball toward a goal that is 29.8 m in front of him. The ball leaves his foot at a speed of 18.9 m/s and an angle of 31.6° above the ground. Find the speed of the ball when the goalie catches it in front of the net. (Note: The answer is not 18.9 m/s.)

Answer 1

This seems to be a projectile motion problem.

State all of your givens first.

d=29.8

Vi=18.9

Theta=31.6

Use a projectile motion equation to find "t" first.

xf=xi+Vit

*isolate t*

xf-xi=Vit

t=(xf-xi)/Vi

t=29.8/18.9

t=1.58

Now that we have time, lets use another projectile motion equation to find the final velocity. But first we need to break up the initial velocity into it's X and Y components.

18.9cos(31.6)=x

18.9sin(31.6)=y

*NOTE! While looking at the vectors on the graph! What ever axis theta is touching, THAT component gets cosine!* (a little trick)

x=18.6

y=3.46

Now lets use an equation to find the vinal velocity.

Vfx=Vix+gt

Vfx=18.6+(9.81)(1.58)

*The acceleration due to gravity is 9.81 m/s^2!!!*

Vfx=34.0998

Vfy=Viy+gt

Vfy=3.46+(9.81)(1.58)

Vfy=18.9598

Now since these are in x and y components they can be arranged as a right triangle on a graph.  From this we can use Pythagorean Theorm.

Vf^2=Vfx^2+Vfy^2

Vf^2=34.0998^2+18.9598^2

Vf^2=1522.259

Vf=sqrt 1522.259

Vf=39.01613769

So the final velocity is about 39 m/s..

Answer 2

d = 20.8 m

v0 = 18.9

angle = 31.6

vx = 18.9 cos 31.6 = 16m/s