Question

You are kicking a soccer ball on a windy night. The acceleration of the wind in the x direction is 2.0 m/s.

a) When the ball is kicked into the wind (de-accelerated) at the angle pi/2, and initial velocity 40 m/s, how far does the ball travel in the x direction prior to landing?

b) When the ball is kicked with the wind (accelerated), at the same angle and initial velocity, how far does the ball travel in the x direction prior to landing?

c) If the ball is kicked into the wind, and the initial velocity is still the same, what angle should it be kicked at so that the ball lands where it started?

Answer 1

The given problem is similar to a standard projectile motion which usually have acceleration as acceleration due to gravity, conventionally taken in negative direction. In this problem additional acceleration in positive direction should be incorporated.

Let us resolve the equation of motion for axis and axis :

For axis we have three set of equation of motion

Similarly for axis we have

a) For and
and The ball is kicked into the wind so the acceleration .
To calculate time distance traveled by the ball first we need to find the time of flight. For that consider the first equation of axis. At top , so

The time of flight of ball is

So the distance traveled in direction is given by,

Therefore the ball lands behind where it was kicked.

b) Using the similar values except the ball is kicked with the wind, which makes the acceleration

Therefore the ball lands in front from where it was kicked.

c) To land the ball where it started we can consider the second equation of axis,

Put then we get

where

Therefore one should kick the ball with an angle for the ball to land there itself.