Jean threw a disc in the air. The height of the disc can be modelled by the function h = -5t^2 + 31.5t + 2, where h is the height in metres after t seconds.
Patrick fired a paintball at the disc. The path of the paintball is modelled by the function h = 30t + 1, with the same units. How long will it take the paint ball to hit the disc?

It will take 0.62 seconds for the paint ball to hit the disc.

Step-by-step explanation:

Height of the disk:

Height of the paintball:

When the paintball will hit the disk?

When they are at the same height, so:

Solving a quadratic equation:

Given a second order polynomial expressed by the following equation:

.

This polynomial has roots such that , given by the following formulas:

In this question:

Quadratic equation with

So

Time is a positive measure, so 0.62.

It will take 0.62 seconds for the paint ball to hit the disc.

the circle one

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