Question

Frank kicks a soccer ball off the ground and in the air, with an initial velocity of 30 feet per second. Using the formula H(t) = −16t2 + vt + s, what is the maximum height the soccer ball reaches?

Answer 1

The answer is A or 14.1

Answer 2

Answer:

A quadratic equation is in the form of $ax^2+bx+c =0$ then the axis of symmetry is given by:

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

Given the equation:

$H(t) = -16t^2+vt+s$

where,

v is the initial velocity

s is the initial height.

Frank kicks a soccer ball off the ground and in the air, with an initial velocity of 30 feet per second.

⇒$v(0) = 30$feet per second.

Substitute in [1] we have;

$H(t) = -16t^2+30t$             ....[1]

then:

the axis of symmetry is:

$t = \frac{-30}{2(-16)} = \frac{30}{32} = 0.9$ sec

Substitute in [1]  we have;

$H(0.9) = -16(0.9)^2+30(0.9)$

⇒ $H(0.9) = -12.96+27$

⇒ $H(0.9) \approx 14.1$  feet

Therefore,the maximum height the soccer ball reaches is, 14.1 feet