Projectile thrown from car

1. The problem statement, all variables and given/known data

A car is driving 40 m/s north on a flat surface when the driver throws a ball out the window. The ball leaves his hand moving horizontally and perpendicular to the car with a speed of 20 m/s with respect to the car.



At the moment the ball leaves the driver's hand, it is 1m above ground. Find the total distance traveled by the rock between its release and the instant it hits the ground. Neglect air resistance or any other forces other than the weight of the ball.



2. Relevant equations

Kinematics:



y = V_ot + (1/2)at²

V_f = V_o + at

V_f² = V_o² + 2ay

y = t * [ (V_o + V_f) / 2 ]



Gravity is 9.82 m/s^2



3. The attempt at a solution



Vector algebra says the initial velocity of the ball is sqrt(40^2 + 20^2) = 44.7 m/s



The final velocity will be 0 m/s I believe.



I've tried a bunch of weird things with Kinematics but I keep getting results that are way off from what is reality. Projectile motion is usually not that difficult for me but that's because I always have the time. In this case I don't so I have to solve for time before doing much else.



y = V_ot + (1/2)at²



y = 44.7t - 4.91 m/s² * t²



Without knowing distance I can't solve for the time here.



Using V_f = V_o + at gave me a weird answer that I knew was wrong. It won't take over 4 seconds to hit the ground I'd think.



Not sure where to go from here...