Independent Practice Use the vertical motion formula h = –16t2 + vt + c.

A soccer ball is kicked with a starting upward velocity of 50 ft/s from a starting height of 3.5 ft. Substitute the values into the vertical motion formula and let h = 0. Use the quadratic formula to solve for t. If no one touches the ball, how long is the ball in the air?

A.
0.1 s

B.
–0.1 s

C.
3.2 s

D.
1.1 s

   The answer is letter A.  0.1s I think

-16t^2 + 50t + 3.5= 0

Step-by-step explanation:  The answer is either letter A or letter B

Question

Use the vertical motion formula h=-16 t^{2}+v t+ch=−16t  

2

+vt+c. A soccer ball is kicked with a starting upward velocity of 50 ft/s from a starting height of 3.5 ft. Substitute the values into the vertical motion formula Let h = 0.

Explanation

Step 1

1 of 2

The starting velocity is 50 ft/s ,when the ball is 3.5 ft high

So, v=50v=50 , h=3.5h=3.5 , t=0t=0

\begin{align*} h&=-16t^2+vt+c &&\text{{\color{#c34632}The vertical motion formula}} 3.5&=-16(0)^2+50(0)+c &&\text{{\color{#c34632}Substitute 3.5 for $h$ , 50 for $v$ , 0 for $t$}} c&=3.5 &&\text{{\color{#c34632}Simplify}} \end{align*}

h

3.5

c

​

=−16t  

2

+vt+c

=−16(0)  

2

+50(0)+c

=3.5

​

​

The vertical motion formula

Substitute 3.5 for h , 50 for v , 0 for t

Simplify

​

So, the vertical motion formula will be

h= -16t^2 + 50t + 3.5

Let h= 0

                                     -16t^2 + 50t + 3.5= 0