A stone is thrown horizontally from the top of a 20-m high hill. It strikes the ground at an angle of 45◦ . With what speed was it thrown?
projectile motion is symmetric
The Attempt at a Solution
I got the answer 277.539 by treating this is a projectile motion problem where the stone is thrown upwards from the ground at a 45 degree angle (since the stone lands at a 45 degree angle it should depart the ground with the same angle since projectile motion is symmetric). I then made some equations for acceleration velocity and position in two dimensions. I solved for time when the y velocity was 0 (this is the midpoint/highpoint of the projectile path). This time value is in terms of the magnitude of the initial velocity. I plugged this time value in to the position in y equation and set it equal to 20 (20 is the height of the rock at the midpoint because the problem says that the rock is thrown off the rock horizontally implying that at this point there is no y velocity and that it is the high point of the path of motion). I solve for the magnitude of the initial velocity and get 40g+1/2. Then, I take this magnitude and multiply it by the cosine of 45 degrees since the components of a vector equals the magnitude times the cos(angle) sin(angle) and I use cos since I'm looking for the x component of the initial velocity. My final answer ends up being 277.5394 m/s. According to this practice test the correct answer is 20. I really don't get how what I did is incorrect. If someone could point out the flaw in my logic I'd be super thankful. Thanks!