What is the average speed of a ball thrown vertically upward at 19.6m/s?
The average velocity of an object is given by:
Average velocity = total displacement / total time
Calculation of Average Speed
Firstly, we need to calculate the time taken for the ball to reach its maximum height. This happens when the final velocity is 0.
Using the equation of motion:
Final velocity (Vf) = Initial velocity (Vi) + acceleration * time
0 = 19.6 - 9.81 * t
Solving for time (t), we find:
t = 2 seconds
The total trip consists of 2 seconds going up and 2 seconds coming down. So, the total trip time is 4 seconds.
Next, we calculate the total displacement of the ball using the formula:
Displacement (s) = Initial velocity (u) * time (t) + 0.5 * acceleration (a) * time (t)²
Substitute the values:
s = 19.6 * 2 - 0.5 * 9.81 * 2²
s = 19.6 meters
Since this is the distance to the maximum height, the total height is twice that value:
Total height = 19.6 * 2
Total height = 39.2 meters
Finally, we can find the average velocity by dividing the total displacement by the total time:
Average velocity = 39.2 / 4
Average velocity = 9.8 m/s
Explanation: The average speed of the ball during its complete trip is 9.8 meters per second. This means that, on average, the ball travels at a speed of 9.8 m/s throughout its journey. The calculation involves determining the total displacement, which accounts for the distance traveled by the ball, and then dividing it by the total time taken for the entire trip. In this specific scenario, the ball's initial velocity, acceleration due to gravity, and total time of travel are key factors in finding the average speed. By applying the formulas of kinematics, we are able to accurately determine the average velocity of the ball thrown vertically upward.
Hope this explanation clarifies the concept and calculation process involved in determining the average speed of the ball. Happy Halloween!