Olympic Kinematics Problem: Reaching the Goal in Time

[KrolKuabV]

Summary: Olympic problem from kinematics

Hello,
could anyone help me with the following problem? I don't quite get how exactly does it work.

After being kicked by a footballer, a ball started to fly straight towards the goal at velocity v = 25m/s making an angle α = arccos 0.8 with the horizontal. Due to side wind blowing at u = 10 m/s perpendicular the initial velocity of the ball, the ball had deviated from its initial course by s = 2 m by the time it reached the plane of the goal. Find the time that it took the ball to reach the plane of the goal, if the goal was situated at distance L = 32 m from the footballer.

This problem is from this PDF https://www.ioc.ee/~kalda/ipho/kin_ENG.pdf . Thanks for any help!

 

[PeroK]

As per PF rules you need to show your best attempt.

Hint: if the wind affects the ball in the transverse direction, what can you say about motion in the other directions?

 

[RoloJosh16]

As per PF rules you need to show your best attempt.

Hint: if the wind affects the ball in the transverse direction, what can you say about motion in the other directions?

It is not affected(?)

 

[haruspex]

It is not affected(?)

It depends how you read this:
"side wind blowing at u = 10 m/s perpendicular the initial velocity of the ball,"
If you read that as meaning the relative velocity is perpendicular to the motion of the ball then, yes, it only exerts a sideways force, so does not affect the velocity component in the original direction. I.e., in the ground frame, the wind has the same forward velocity as the ball (25 cos(α)m/s), plus a 10m/s crosswind component.
This still does not quite work because the wind would still have a vertical relative velocity, vertically downward initially, vertically upward later. This will tend to slow the forward motion of the ball.
However, I don't think the author considered that it needs to be specified as relative.