I have the following problem:
A projectile of mass m is launched from the origin at time t=0, with speed U, at an angle of elevation a+b to the horizontal. The launch site lies on a ramp that makes an angle b to the horizontal (You are given that 0<a<Pi/4 and 0<b<Pi/4)
During its flight, the projectile is subject to two forces, a gravitational force of magnitude mg, vertically downwards and a drag force -m*k*v, where v is the velocity of the projectile and k>0 is a constant.
a)Derive that the coordinates of the projectile are:
b) Show that the projectile lands on the ramp when the time t satisfies
I have done part a by using Newton's second law and by solving two secodn order differentials equations and by applying the initial conditions.
Now I am trying to do part b and I am struggling to understand where did sina came from, since when the projectile land on the ramp our angle equals to b. I tried substituting in the x,y coordinates of the projectile (a+b)=b but I am not guided anywhere. How is the angle a related with the answer since when the projectile lands on the ramp is at angle b from the origin?? (since the ramp is on angle b)
I will appreciate any help and guidance for solving part b!