Explanation:
To hit the ball with the bumper, the ball needs to move towards the bumper.
The distance between the ball and the bumper is 8 - (-5) = 13 units.
Assuming the bumper is stationary, let's calculate the minimum force needed to move the ball towards the bumper.
We can use the formula:
force = mass x acceleration
The mass of the ball is not given, so let's assume it to be 1 unit.
The acceleration needed can be calculated using:
acceleration = (final velocity - initial velocity) / time
Let's assume that the time taken for the ball to reach the bumper is 1 second.
The initial velocity of the ball is 0 units (assuming it is stationary).
The final velocity needed to reach the bumper can be calculated using:
final velocity^2 = initial velocity^2 + 2 x acceleration x distance
final velocity^2 = 0 + 2 x acceleration x 13
final velocity^2 = 26 x acceleration
Since we want to hit the ball with the bumper and not destroy it, let's assume that the final velocity needed to reach the bumper is 1 unit per second.
Substituting this value in the equation above:
1^2 = 26 x acceleration
acceleration = 1 / 26 units per second^2
Substituting the values of mass and acceleration in the formula for force:
force = mass x acceleration
force = 1 x (1 / 26)
force = 1 / 26 units
Therefore, the minimum force needed to hit the ball with the bumper and collect the star is 1/26 units.