Two dimensional motion problem (kicking a soccer ball into the goal)

[Ineedhelpwithphysics]

Homework Statement

Carli Lloyd scored half-field goal (53 m) vs. Japan with a beautiful projectile motion. It looks from the video that the ball was inthe air for 2.0 seconds. What was the angle of the ball when it left her foot?

Relevant Equations

VoX = vcos(theta)
VoY = vsin(theta)
Vf(y) = Vo(y) + a(y)t
Delta y = VoY + 1/2a(y)t^2

I did this too fast idk if I'm wrong

So for the x component
use the formula d = rt / delta x = v*t
26 = vcos(theta)

y component
use the displacement formula
19.6 = vsin(theta)

tan^-1(19.6/26) = 36.5 degrees
the answer key says 20.2 degrees idk whats wrong

 

[Ineedhelpwithphysics]

I did wrong calculations please ignore this

 

[Delta2]

I get the angle 20.67 with ##g=10m/s^2##.
Your first equation is almost correct, it should be $$\frac{53}{2}=v_0\cos\theta$$
But no clue how did you infer the 2nd equation.
Hint: if the total flight time is 2.0 sec what is the total ascent time, ##t_A## ,that is the time the ball rises from the initial point to its highest point, and how ##v_{0y}=v_0\sin\theta## relates to ##t_A##?

Now I see that your second equation is also almost..... correct up to a factor of 2 e hehe and with ##g=9.8m/s^2##

 

[brotherbobby]

What is the formula the for range ##R## of a projectile and its total time of flight ##T##? Those two are the ones you need to answer the question @Ineedhelpwithphysics