Question

Lucy kicks a shuttlecock into the air from a height of 0.6 feet
with an initial vertical velocity of 16 feet per second. Use the
vertical motion model, h = -16t2 + vt + s, where v is the
initial velocity in feet per second and s is the initial height in
feet, to calculate the maximum height of the shuttlecock.
Round your answer to the nearest tenth if necessary.
Maximum height: ___feet

Answer 1

Answer:

4.6 feet

Step-by-step explanation:

The equation is:

$h=-16t^2+vt+s$

Where

v is initial velocity (given as 16)

s is initial height (given as 0.6)

Substituting, we can write:

$h=-16t^2+16t+0.6$

This is a quadratic equation of the general form:  $at^2+bt+c$

Which we can conclude the coefficients to be:

a = -16

b = 16

c = 0.6

The max height occurs at the value:  $t=-\frac{b}{2a}$

So, max height occurs at:

$t=-\frac{16}{2(-16)}\\t=0.5$

We will get the max height if we put  t = 0.5  into the original equation. So that would be:

$h=-16t^2+16t+0.6\\h=-16(0.5)^2+16(0.5)+0.6\\h=4.6$

Max Height = 4.6 feet   (occurs at t = 0.5 seconds)