Question

A rock is tossed vertically from a height of 2m with an initial velocity of 20 ms-1. The height of the rock, h, after t seconds can be modeled by the polynomial function :h(t)=−4.9t2+20t+2, t≥0. Calculate how many seconds, rounded to three significant figures, it takes for the rock to hit the ground.

Answer 1

Answer:

The rock takes 4.18 seconds to hit the ground

Step-by-step explanation:

Function Model

The height of a rock h, after t seconds, can be modeled by the polynomial function:

$h(t)=-4.9t^2+20t+2, t\geq 0$

When the rock hits the ground, the height is 0, thus we need to find the value of t such as:

$-4.9t^2+20t+2=0$

A quadratic equation can be expressed as:

$at^2+bt+c=0$

where a,b, and c are constants.

Solving with the quadratic formula:

$\displaystyle t=\frac{-b\pm \sqrt{b^2-4ac}}{2a}$

The values for the given equation are:

a=-4.9, b=20, c=2

Applying the formula:

$\displaystyle t=\frac{-20\pm \sqrt{20^2-4(-4.9)(2)}}{2(-4.9)}$

$\displaystyle t=\frac{-20\pm \sqrt{400+39.2}}{-9.8}$

$\displaystyle t=\frac{-20\pm 20.957}{-9.8}$

There are two possible solutions:

$\displaystyle t=\frac{-20- 20.957}{-9.8}=4.18$

$\displaystyle t=\frac{-20+ 20.957}{-9.8}=-0.1$

Since t > 0, the only solution is t=4.19 seconds

The rock takes 4.18 seconds to hit the ground