The heigh b that a basketball will bounce on a hardwood floo

The heigh, b, that a basketball will bounce on a hardwood floor varies with the height,h, from which the ball is dropped. A basketball dropped from 5 feet will bounce 2.8 feet. Write an equation that relates b to h.

Solution

To solve this question you should be aware of the following result.
\"Given two quantities y and x where y varies directly with x then the relationship between y and x can be written as: y=kx where k is a constant\".
Since the bounce varies DIRECTLY with the height from which it is dropped then the relationship between the height and bounce can be expressed as
b=k*h (i)
where h= the height from which the ball is dropped,b=the height of the bounce and k= a constant value.
In order to find the equation that links b to h we must find the value of the constant k.
To do this we use the rest of the given information which is that when the ball is dropped from 5 feet the bounce is 2.8 feet.
This means that when h=5,b is equal to 2.8.
Knowing this means that we can now replace h and b in equation (i) by these values so that the equation becomes:
2.8=k*5 or 5k=2.8
Now share both sides of the equation by 5 and we get:
k=2.8/5=5.6/10=0.56
Hence the equation b=k*h can now be written as b=0.56h ANS