Question

Michelle throws a frisbee into the air. The height of the frisbee at a given time can be modeled by the equation h(t)= -2t

Answer 1

Answer:

(a) The ball will hit the ground after 3 seconds

(b) The maximum height is 6.125

Step-by-step explanation:

Given

$h(t) = -2t^2 +5t +3$

Solving (a): When the frisbee will hit the ground?

To do this, we set h(t) to 0

So, we have:

$h(t) = -2t^2 +5t +3$

$-2t^2 +5t +3=0$

Expand

$-2t^2 +6t-t +3=0$

Factorize

$-2t(t - 3) -1(t - 3) = 0$

Factor out t - 3

$(-2t -1)(t - 3) = 0$

Split:

$-2t -1= 0\ or\ t - 3 = 0$

Solve for t in both equations

$-2t =1\ or\ t = 3$

$t =-\frac{1}{2}\ or\ t = 3$

Time can't be negative; So:

$t = 3$

Solving (b): How height the frisbee will go?

First, we calculate time to reach the maximum height

$t = -\frac{b}{2a}$

Where:

$h(t) = at^2 + bt + c$

By comparison:

$a = -2,\ b =5,\ c =3$

So:

$t = -\frac{b}{2a}$

$t = -\frac{5}{2*-2}$

$t = \frac{5}{4}$

$t = 1.25$

So, the maximum height is:

$h_{max} = -2 * 1.25^2 + 5 * 1.25 + 3$

$h_{max} = 6.125$