Question

3. A ball was thrown into the air with an initial velocity of 72 feet per second. The height of the

Answer 1

Answer:

A. The maximum heigh is 81 feet

B. The ball will reach the maximum heiight at 2.25 seconds

C. The domain of the function is $t\in [0,4.5]$

D. The range of the function is $h(t)\in [0,81]$

E. 4.5 seconds

Step-by-step explanation:

A ball was thrown into the air with an initial velocity of 72 feet per second. The height of the ball after t seconds is represented by the equation:

$h= -16t^2 + 72t$

The maximum height will be at parabola's vertex. Find it:

$t_v=\dfrac{-b}{2a}\\ \\t_v=-\dfrac{72}{2\cdot (-16)}=\dfrac{72}{32}=\dfrac{9}{4}=2.25\\ \\h(t_v)=-16\cdot t_v^2+72\cdot t_v\\ \\h(2.25)=-16\cdot 2.25^2+72\cdot 2.25=81$

A. The maximum heigh is 81 feet

B. The ball will reach the maximum heiight at 2.25 seconds

C. Find where the parabola intersects the x-axis:

$h=0\Rightarrow -16t^2+72t=0\\ \\t(-16t+72)=0\\ \\t_1=0\ \text{or}\ 16t=72,\ t_2=\dfrac{9}{2}=4.5$

So, the domain of the function is $t\in [0,4.5]$

D. The range of the function is

$h(t)\in [0,81]$

E. The ball is at the air for 4.5 seconds