Writing two Second-Order equations as a System of First-Order Equations
I'm just looking over some stuff as revision because I have exams soon and I'm a bit confused about this question.
Consider a tennis ball that is thrown upwards at time t = 0, with an initial speed U at an angle theta to the horizontal. From Newton's second law, the equations of motion (neglecting air resistance) can be written as follows:
(d^2)x/d(t^2) = 0
(d^2)y/d(t^2) = -g
Rewrite each of the above second-order differential equations as 2 first-order differential equations.
No matter how many different ways I try it, I end up with only one first-order differential equation for each of these equations and can't find a second one. Essentially, I always get dx/dt = c, and dy/dt = gt + c. I'm probably being really stupid here, but please help.