Question

8 A test rocket is fired and follows a path described by y = 0.1x(200 – x). The height is y metres above

ground and x is the horizontal distance in metres.
How far does the rocket travel horizontally?
b How high does the rocket reach mid-flight?

Answer 1

a) The rocket travels 200 meters horizontally.

b) The height of the rocket mid-flight is of 1000 meters.

Explanation:

Height of the rocket:

The height of the rocket, in meters, after an horizontal distance of x, is given by:

`y = 0.1x(200 - x)`

a) How far does the rocket travel horizontally?

This is x when
`y = 0`. So

`0.1x(200 - x) = 0`

Then

`0.1x = 0`

`x = 0`

And

`200 - x = 0`

`x = 200`

So

The rocket travels 200 meters horizontally.

b How high does the rocket reach mid-flight?

This it the height y when x = 0, so:

`y = 20*100 - 0.1*100^2 = 1000`

The height of the rocket mid-flight is of 1000 meters.