A ball is rolling over a soccer field with constant velocity Vb > 0 at an angle of 45° to the goal line. It starts at the corner of the field (distance d from the middle of the goal line) at the time t0 = 0. At the same time a player starts heading towards the goal on a path perpendicular to the goal line. He starts from a position at distance 2d in front of the middle of the goal line) with ap(t) = a0 (1− (t/ß))

I've solved the problems but the left thing to do is just the initial acceleration. I use integration to find these solutions:

- Distance covered by the ball sb=Vb*t

- Time when ball is in front of the middle of the goal line tA = 2√d / Vb (with distance sA = d / cos45°)

- Velocity of player vp = a0 (t − (t^1/2ß))

- Distance covered by the player sp = a0 / 6*ß (3ßt^2−t^3)

- Velocity of the player when he reach the point (the point after the ball reach distance sA) vpA = a0*d / vb (√2 − (d/vb*ß)) *I'm inserting tA into vp, am I right?

- Initial acceleration of the player in order to reach the point (the point after the ball reach distance sA) at the same time as the ball a0 = ??

Any ideas would be very appreciated. Thanks.

I've solved the problems but the left thing to do is just the initial acceleration. I use integration to find these solutions:

- Distance covered by the ball sb=Vb*t

- Time when ball is in front of the middle of the goal line tA = 2√d / Vb (with distance sA = d / cos45°)

- Velocity of player vp = a0 (t − (t^1/2ß))

- Distance covered by the player sp = a0 / 6*ß (3ßt^2−t^3)

- Velocity of the player when he reach the point (the point after the ball reach distance sA) vpA = a0*d / vb (√2 − (d/vb*ß)) *I'm inserting tA into vp, am I right?

- Initial acceleration of the player in order to reach the point (the point after the ball reach distance sA) at the same time as the ball a0 = ??

Any ideas would be very appreciated. Thanks.

Last edited: