A ping pong ball is rolling across a table top at 22 m/s. If it is 71 m away from the edge, how much acceleration does a person blowing on it need to apply to stop it from falling if they blow for 8.7 seconds?
To answer this question, we need to determine the initial velocity (v0) of the ping pong ball, the final velocity (vf) we want to achieve (which is 0 in this case), the time duration (t) for which the acceleration is applied, and use the equation of motion to calculate the acceleration (a) required.
Given:
Initial velocity (v0) = 22 m/s
Final velocity (vf) = 0 m/s
Time duration (t) = 8.7 seconds
The equation of motion that relates acceleration, time, initial velocity, and final velocity is as follows:
vf = v0 + a*t
Since the final velocity, vf, is 0, we can simplify the equation to:
0 = 22 + a * 8.7
Now, let's solve for the acceleration (a):
0 = 22 + 8.7a (Distribute the a)
-22 = 8.7a (Subtract 22 from both sides)
a = -22/8.7 ≈ -2.53 m/s²
Therefore, the person blowing on the ping pong ball needs to apply an acceleration of approximately -2.53 m/s² (negative since the acceleration is opposing the motion) to stop it from rolling off the edge of the table.