A ping pong ball is rolling across a table at 22 cm/s. When the ball is 78 m away from the edge your little brother starts to blow on it. If the little doofus hopes to prevent the ball from falling off the edge, what minimum acceleration must be achieved?
To find the minimum acceleration required to prevent the ball from falling off the edge, we need to determine the time it takes for the ball to reach the edge and the distance traveled during that time.
First, let's convert the distance from meters to centimeters:
78 m = 78 * 100 cm = 7800 cm
Now, let's find the time it takes for the ball to reach the edge. We can use the equation: distance = velocity * time.
distance = 7800 cm
velocity = 22 cm/s
Rearranging the equation, we have:
time = distance / velocity
time = 7800 cm / 22 cm/s = 354.55 s
Next, let's find the distance traveled during that time. We can use the equation: distance = initial velocity * time + (1/2) * acceleration * time^2.
distance = ?
initial velocity = 0 (since the ball starts rolling from rest)
time = 354.55 s
acceleration = ?
Rearranging the equation and plugging in the values, we have:
distance = (1/2) * acceleration * time^2
7800 cm = (1/2) * acceleration * (354.55 s)^2
Now, let's solve for acceleration:
acceleration = (2 * distance) / (time^2)
acceleration = (2 * 7800 cm) / (354.55 s)^2
acceleration ≈ 0.314 cm/s^2
Therefore, in order to prevent the ball from falling off the edge, a minimum acceleration of approximately 0.314 cm/s^2 must be achieved by your little brother blowing on the ball.