the height that a ball bounces varies directly as the height from which it is dropped. A ball dropped from a height of 20cm bounces 16cm

a) Find the height of the bounce if the ball is dropped from a height of 280cm

b) Find from waht height the ball was dropped if it bounces to a height of 120cm

Thanks in advance.

let h be the new height, let x be the height it was dropped from, then

h = kx, where k is a constant
when x=20, h=16
so 16=k20
k = 16/20 = 4/5
then h =4x/5

a)when x= 280
h = 4(280)/5 = 224

b) when h = 120
120 = 4x/5
600 = 4x
x = 150

a) Well, if the height that a ball bounces varies directly with the height from which it is dropped, we can use a proportion to find the height of the bounce. Let's call the height of the bounce "h" and the height from which it is dropped "d". We can set up the proportion:

h/16 = 280/20

Cross-multiplying, we get:

h = (16 * 280) / 20

Simplifying, we find:

h = 224 cm

So, the height of the bounce when the ball is dropped from a height of 280 cm is 224 cm.

b) Now, let's find the height from which the ball was dropped if it bounces to a height of 120 cm. Again, setting up a proportion:

120/16 = d/20

Cross-multiplying:

d = (20 * 120) / 16

Simplifying:

d = 150 cm

Therefore, the ball was dropped from a height of 150 cm if it bounces to a height of 120 cm.

Hope that helps!

a) To find the height of the bounce if the ball is dropped from a height of 280cm, we can set up a proportion using the direct variation relationship between the height of the bounce and the height from which it is dropped.

Let's denote the height of the bounce as x. According to the given information, we have the following proportion:

(20 cm / 16 cm) = (280 cm / x)

To solve for x, we can cross multiply:

20 cm * x = 16 cm * 280 cm

Simplifying the right side of the equation:

20x = 16 * 280

20x = 4480

Dividing both sides by 20:

x = 4480 / 20

x = 224 cm

Therefore, the height of the bounce when the ball is dropped from a height of 280 cm is 224 cm.

b) To find from what height the ball was dropped if it bounces to a height of 120 cm, we can use the same direct variation proportion:

(20 cm / 16 cm) = (x cm / 120 cm)

Cross multiplying:

20 cm * 120 cm = 16 cm * x cm

2400 cm = 16x

Dividing both sides by 16 cm:

x = 2400 cm / 16 cm

x = 150 cm

Therefore, the ball was dropped from a height of 150 cm if it bounces to a height of 120 cm.

To solve these problems, we need to use the direct variation relationship between the height of the bounce and the height from which the ball is dropped.

We can set up a proportion to solve both parts of the problem:

h₁ / d₁ = h₂ / d₂

Where:
h₁ is the height of the bounce for the first scenario
d₁ is the height from which the ball is dropped in the first scenario
h₂ is the height of the bounce for the unknown scenario
d₂ is the height from which the ball is dropped in the unknown scenario

Now let's solve each part of the problem:

a) Find the height of the bounce if the ball is dropped from a height of 280cm.

Given:
h₁ = 16cm (height of the bounce for the first scenario)
d₁ = 20cm (height from which the ball is dropped in the first scenario)
d₂ = 280cm (height from which the ball is dropped in the unknown scenario)

Using the proportion:

16 / 20 = h₂ / 280

To solve for h₂, we cross-multiply and divide:

16 * 280 = 20 * h₂
4480 = 20h₂
h₂ = 4480 / 20
h₂ = 224cm

Therefore, the height of the bounce when the ball is dropped from a height of 280cm is 224cm.

b) Find from what height the ball was dropped if it bounces to a height of 120cm.

Given:
h₁ = 16cm (height of the bounce for the first scenario)
d₁ = 20cm (height from which the ball is dropped in the first scenario)
h₂ = 120cm (height of the bounce in the unknown scenario)
d₂ = unknown

Using the proportion:

16 / 20 = 120 / d₂

To solve for d₂, we cross-multiply and divide:

16 * d₂ = 20 * 120
16d₂ = 2400
d₂ = 2400 / 16
d₂ = 150cm

Therefore, the ball was dropped from a height of 150cm if it bounces to a height of 120cm.

I hope this helps! Let me know if you have any further questions.