Question

A purple ball rolls off a horizontal table with an initial speed of $3.0m/s$. A red ball rolls off the same table with an initial speed of $1.5m/s$. Both balls fly undhindered toward the horizontal floor that they hit at some horizontal distance from the edge of the table.
How does the horizontal distance for the purple ball compare to the horizontal distance for the red ball?

• A. The horizontal distance for the purple ball is twice as much as that for the red ball
• B. The horizontal distance for the purple ball is the same as the horizontal distance for the red ball
• C. The horizontal distance for the purple ball is four times as much as that for the red ball
• D. The horizontal distance for the purple ball is half as much as that for the red ball
• E. We need to know the relative masses of the balls to answer this question

Answer 1

The correct option is A The horizontal distance for the purple ball is twice as much as that for the red ball

As both the balls are in free fall therefore they will take equal time to reach to the floor if air resistance is neglected , let the time taken is $t$ ,

now horizontal distance for purple ball $x_p=3.0\times t$ ,

horizontal distance for red ball $x_r=1.5\times t$ ,

therefore , $x_p/x_r=3.0/1.5=2$ ,

or $x_p=2x_r$

the horizontal distance for purple ball is twice of the red ball .