Projectile motion?

Question

A soccer player kicks the ball toward a goal that is 28.6 m in front of him. The ball leaves his foot at a speed of 19.3 m/s and an angle of 31.0° above the ground. Find the speed of the ball when the goalie catches it in front of the net. (Note: The answer is not 19.3 m/s.)

Heres what I've done:

1st-found Vx
Vocos(31)
(19.3m/s)*(cos31)=16.543m/s

2nd-found Vy
x=Vo*xt
t=(vox)/(x)
28.6/16.543=1.729s

3rd-Voy
Vosin(31)
(19.3m/s)(sin31)=9.940m/s
NOT SURE! if the time is right>>>>>Vy=Voy+at
9.940+(9.80m/s^2)(1.729)=26.8842

Last step! square root(916.5430^2)+(26.8842^2)
=31.56m/s<<
I DONT KNOW WHAT I HAVE DONE WRONG! I THINK THAT THE ANSWER FOR Voy NEEDS TO BE SMALLER .

Answer 1

you need to explain why you use those equation because i don't really get what you are saying. But here is how you do it.

you got it right when you found Vx = 16.543m/s and Vy = 9.94m/s

Now you need to find the time it takes the ball to travel infront of the net
x = vt
28.6m = (16.543m/s)t
t = 1.729s

now you need to find the vertcal velocity of the ball at 1.729s
Vf = at + Vi
Vf = (-9.8) (1.729) + 9.94
Vf = -7 m/s

now that you have to horizonal velocity and vertical veloicity, pythagarian theorem

a^2 + b^2 = c^2
(-7)^2 + (16.543)^2 = c^2
c = 17.963 m/s

What you did wrong is when you find Voy you use a positive acceleration. Acceleration due to the Earth is always negative (-) 9.8m/s. Plus, we are dealing velocity, not speed, at 1.792s, the ball is falling downward, that's why we have a -7m/s at 1.792s. So that 's your error right there

Answer 2

V is a vector
Vx(0) =19.3 cos 31=16.54m/s and remains constant Vy(0)= 19.3sin31=9.94m/s
Vy(t) =-9.8t+9.94m/s
28.6=16.54t ( time to reach the goal
t=1.73 s
at this time Vy = -7m/s(downwards)
Speed = sqrt(7^2+16.54^2)=17.96m/s
You forgot that acceleration is a vector and in this case directed downwards

Answer 3

In your 3rd step, you use the formula v = u + at.
But in this case, a = -g. Don't forget that negative sign.

If you use the negative sign, you'd get
voy = -7.02 m/s when the GK catches it.
vox = 16.54 m/s as you have it.

So resultant speed = sqrt(7.02^2 + 16.54^2) = 17.97 m/s