To find the velocity of a ball when it is thrown upward and then falls back down, we need to consider the principles of motion and the effects of gravity. Here's a step-by-step explanation:
Start by determining the initial velocity (v₀) with which the ball is thrown upward. This could be given in the problem or measured directly.
Due to the force of gravity, the ball will experience a constant downward acceleration (a) throughout its motion. On Earth, the acceleration due to gravity is approximately 9.8 m/s², directed downward.
As the ball travels upward, it will gradually slow down until it reaches its highest point. At this point, the ball momentarily comes to a stop before falling back down. Let's call the highest point the peak.
At the peak of the ball's motion, its velocity is zero. This occurs because the upward velocity decreases until it is completely overcome by gravity, causing the ball to momentarily stop before reversing direction.
On the way down, the ball will accelerate due to gravity. The acceleration due to gravity acts in the downward direction, so the ball will experience an acceleration of approximately 9.8 m/s².
To find the velocity of the ball at any given point during its fall, we can use the equation for motion under constant acceleration:
v = v₀ + at,
where v is the final velocity, v₀ is the initial velocity, a is the acceleration, and t is the time.
Since we want to find the velocity when the ball hits the ground, we need to find the time it takes for the ball to fall from the peak to the ground. To do this, we can use the equation for free fall:
h = (1/2)gt²,
where h is the height of the peak above the ground, g is the acceleration due to gravity, and t is the time taken to fall.
Solve this equation for t to find the time it takes for the ball to fall from the peak to the ground.
Once you have calculated the time taken to fall, substitute the value of time (t) into the equation v = v₀ + at to find the final velocity (v) of the ball when it hits the ground.
Remember to take care with signs when working with upward and downward motion. The initial velocity (v₀) will be positive when throwing the ball upward, while the acceleration (a) due to gravity will be negative since it opposes the upward motion.
By following these steps, you should be able to find the velocity of the ball when it is thrown upward and falls back down.