calculate velocity using parametric functions

Question

if i have the following parametric functions where time is m/s :

x = 8 t 
y = -5 t2 + 6 t

and i want to find the initial velocity can i do the following:

v^2 = 8^2 + 6^2
v^2 = 100
v = 10 m/s 

is this correct?

also if i were to add in air friction into the horizontal movement (but not into the vertical movement) how would i go about calculation velocity now?

lets say x is now:

x = 8t -0.1t^2

Answer 1

yeah you are correct but it is better to do it like this.. $dx/dt = 8$ and $dy/dt = -10t+6$ here, the $x$-component of velocity is constant therefore initially also it will be 8. And the $y$-component of velocity varies with time, therefore we put $t=0$ to get initial vertical velocity which comes out to be 6. Now, $v^2 =(dx/dt)^2$ at $t=0$ + $(dy/dt)^2$ at $t=0$ which gives magnitude of initial velocity = 10. Now, calculating velocity when there is air friction becomes easy when we follow this approach.