A student throws a ball vertically upward such that it travels 6.8m to its maximum height. What is the average speed? What is the average velocity?
To find the average speed and average velocity, we need to understand the concept of speed and velocity and how they differ.
Speed is a scalar quantity that represents how fast an object is moving, regardless of its direction. It is calculated by dividing the total distance traveled by the total time taken. The formula for average speed is:
Average Speed = Total distance / Total time
On the other hand, velocity is a vector quantity that includes both speed and direction. It represents the rate at which an object changes its position. Average velocity takes into account the displacement (change in position) and the total time taken. The formula for average velocity is:
Average Velocity = Displacement / Total time
In the given scenario, the ball is thrown vertically upward and comes back down to its original position. Since the vertical displacement is zero when it reaches its maximum height, the average velocity will also be zero. This means that the average velocity of the ball is zero.
However, to find the average speed, we need to calculate the total distance traveled by the ball.
When the ball is thrown upward, it travels 6.8m to its maximum height. On its way back down, it covers the same distance. Therefore, the total distance traveled is:
Total distance = Distance upward + Distance downward
Total distance = 6.8m + 6.8m
Total distance = 13.6m
Now, we need to determine the time it takes for the ball to reach its maximum height. We can do this by using the equation:
Final velocity = Initial velocity + (Acceleration × Time)
At the highest point, the ball's velocity becomes zero since it comes to a stop before changing direction. The initial velocity at the moment it was thrown upward is the same as the final velocity at the highest point. Thus, we can rewrite the above equation as:
0 = Initial velocity + (-9.8 m/s^2 × Time)
Solving for Time:
-9.8 m/s^2 × Time = -Initial velocity
Time = -Initial velocity / -9.8 m/s^2
Now, remember that the total time taken by the ball is the time it takes to reach the highest point, plus the time it takes to come back down. So, the total time will be twice the time it takes to reach the highest point.
Total time = 2 × Time = 2 × (-Initial velocity / -9.8 m/s^2)
Finally, we can calculate the average speed:
Average Speed = Total distance / Total time
Average Speed = 13.6m / (2 × (-Initial velocity / -9.8 m/s^2))
By plugging in the specific value of the initial velocity, you can calculate the average speed. Keep in mind that the initial velocity is a key variable that needs to be provided in order to obtain a numerical answer.