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

Answer:

a) The rocket travels 200 meters horizontally.

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

Step-by-step 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.