My problem looks like this:
I need to find the point of impact and the time the body traveled.
The Attempt at a Solution
I tried to find the time for 25 meters and with that the vertical velocity and height.
Ended up getting: t at 25m = 1.96 s , h=16.83 m vi=-1.03 m/s
I tried this: hf=vx*sin37*t = 7.67 m/s*t , it should mean that for every seconds the slope rises 7.66m in height.
After that I set up: hf = h + vi*t - 1/2*g*t^2 and got:
7.67*t = 16.83 - 1.03*t - 4.905*t^2
-4.905*t^2 - 8.7*t + 16.83 = 0
4.905*t^2 + 8.7*t - 16.83 = 0
The positive t was 1.17 s
Total time = 1.96 s + 1.17 s = 3.13 s
h = vi*t - 1/2*g*t^2
h = 18.20 m/s * 3.13 s - 1/2 * 9.81 m/s^2 * (3.13s)^2
h = 8.91 m
distance = vx*t
distance = 12.75 m/s * 3.13 s = 39.9 m
My problem is that the height and distance doesn't match, the tangent of the angle is: height/distance = 8.91/39.9-25=8.91/14.9=0.5979 , with arctg I get around 31 degrees, shouldn't I get 37 degrees here? This is what bothers me. Is the method I used correct? If not, what is the method I should use to solve it?