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x = vx * t

y = vy * t + c * t²

vx²+vy² = 1

=>

t² = t² * (vx² + vy²) = (vx t)² + (vy t)² = x² + (y - c t²)²

With T := t², this gives

T = x² + y² - 2 y c T + c² T²

or

c² T² - (2 c y +1) T + (x²+y²) = 0.

This is solveable iff

(2 c y +1)² >= 4 c² (x²+y²)

[or equivalently: (y +1/(2c))² >= x²+y²]

in which case the solutions are

T = ( (2 c y +1) +- sqrt( (2 c y +1)² - 4 c² (x²+y²)) )/(2c²)

The value of t is then +-sqrt(T) for each of these values of T (provided T>=0).

With x = 0.0489781031941, y = -0.0157020445670, we find

T = ( 0.78017 +- sqrt(0.09017) )/98, i.e.

T1 = 0.011025, T2 = 0.004897.

Since both are positive, we obtain a total of four t-values:

t = +- 0.105 and t = +- 0.07