a) Since the ball initially rises to a height of 8, we can write the expression for the height the ball reaches after the nth impact with the ground as:
Height(n) = 8 * (3/4)^(n-1)
b) The total distance that the ball travels from the first throw to the Ath impact with the ground can be calculated by summing up the distances of each upward and downward motion.
Let's denote the total distance traveled as D.
The distance traveled during the first upward motion is 8.
For subsequent motions, the distance traveled during each upward motion is 2 times the height reached after the previous bounce.
Therefore, the distance traveled during the upward motion after the nth bounce is 2 * Height(n-1).
The distance traveled during the downward motion after the nth bounce is equal to the height reached after the nth bounce.
So the total distance D can be expressed as:
D = 8 + 2(Height(1) + Height(2) + ... + Height(A))
To find the value of D, we can substitute the expression for Height(n) from part a:
D = 8 + 2((8*(3/4)^0) + (8*(3/4)^1) + ... + (8*(3/4)^(A-1)))
Simplifying this expression will give us the total distance traveled by the ball.
A ball is thrown vertically upwards from the ground. The ball rises to a height of 8 and then falls and bounces. After each bounce it rises to 3/4 of the height of the previous bounce.
a Write down an expression for the height that the ball rises affor the nth impact with the ground.
b Find the total distance that the ball travels from the first throw to the Afth impact with the ground.
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