A ball is dropped from a height of 30 feet and allowed to bounce until it comes to arrest each time the ball bounces it rebounds to 3/5 of its previous high after which bounce is the boss hi 10.8 feet.
I understand the height gets shorter but is there a equation to solving this I don't know where to start.
Yes, there is an equation you can use to solve this problem. Let's break it down step by step:
Step 1: Define the variables:
Let's call the initial height of the ball before the first bounce "H". In this case, H = 30 feet.
We will also need to define another variable to represent the rebound height after each bounce. Let's call it "r". We know that the ball rebounds to 3/5 of its previous height, so r = (3/5)H.
Step 2: Find the height after each bounce:
After the first bounce, the height of the ball is the rebound height, r.
After the second bounce, the height of the ball is (3/5)r (since it rebounds to 3/5 of the rebound height).
After the third bounce, the height of the ball is (3/5)^2 * r (since it rebounds to 3/5 of the previous rebound height).
And so on...
Step 3: Set up an equation:
We know that the height of the ball after the 10th bounce is 10.8 feet. So we can set up an equation using the information from Step 2:
10.8 = (3/5)^(10-1) * r
Step 4: Solve for "r":
We can now solve the equation for r using algebraic operations. Start by isolating r:
r = 10.8 / (3/5)^(10-1)
Step 5: Evaluate the right side of the equation:
Evaluate the right side of the equation to find the value of r:
r ≈ 10.8 / (0.6)^9 ≈ 0.09375 feet
So, the rebound height after each bounce is approximately 0.09375 feet.
To find the height after each bounce, you can use the equation:
Height after n bounce = (3/5)^(n-1) * r
You can plug in different values of n to find the height after each specific bounce.