What was the direction of the ball’s velocity
just before it hit the floor?
That is, at what angle (in the range −90◦ to
+90◦ relative to the horizontal directed away
from the table) did the ball hit the floor?
Answer in units of ◦.
To determine the direction of the ball's velocity just before it hit the floor, we need more information. We require the initial velocity of the ball, both the magnitude and the direction, in order to calculate the angle at which it hits the floor.
If you have the initial velocity components, one in the horizontal direction and one in the vertical direction, you can use trigonometry to find the angle. The tangent of the angle is equal to the vertical velocity component divided by the horizontal velocity component:
tan(θ) = (vertical velocity component) / (horizontal velocity component)
To find the angle itself, you can take the arctan of this ratio:
θ = arctan((vertical velocity component) / (horizontal velocity component))
If you do not have the initial velocity components, you will need to know either the angle at which the ball was initially launched or the total initial velocity and the angle at which the ball hits the floor. With this information, you can determine the initial velocity components and use the method described above.
Remember to use caution with the signs when calculating the angle. The range of -90° to +90° is relative to the horizontal and directed away from the table. A negative angle would indicate a velocity directed downward toward the floor, while a positive angle would indicate an upward velocity away from the floor.
To determine the direction of the ball's velocity just before it hit the floor, we can analyze the motion of the ball.
Assuming the ball was thrown or dropped vertically downward, it would have been moving in a straight line vertically downward just before it hit the floor.
Since the horizontal direction is perpendicular to the vertical direction, the angle of the ball's velocity relative to the horizontal just before it hit the floor would be 90° directed away from the table.