Select the correct answer. Tara and Mallory are practicing their passing at volleyball practice. Tara bumps the ball from a height of 3 feet above the ground with an initial up velocity of 12 feet/second. At the same time, Mallory serves the ball from a height of 3.25 feet above the ground with an initial upward velocity of 9 feet/second. If $$ x $$ represents the number of seconds since each ball is passed and $$ y $$ represents the height of the ball, which system of equations models the pr motion of the two balls? Recall that the acceleration due to gravity is $$ \mathbf{- 3 2} $$ feet/second. A. $$ y=-16 x^{2}+12 x+3 $$ $$ y=-16 x^{2}+9 x+3.25 $$ B. $$ y=-16 x^{2}+9 x-3 $$ $$ y=-16 x^{2}+12 x-3.25 $$ c. $$ y=-16 x^{2}+12 x-3 $$ $$ y=-16 x^{2}+9 x-3.25 $$ D. $$ y=-16 x^{2}+9 x+3 $$ $$ y=-16 x^{2}+12 x+3.25 $$

Question

UpStudy AI · Accepted Answer

To model the motion of the two volleyballs, we'll use the kinematic equation for vertical motion under gravity:

$$
y = -16x^2 + v_0x + y_0
$$

where:
- $$ y $$ is the height of the ball in feet,
- $$ x $$ is the time in seconds,
- $$ v_0 $$ is the initial upward velocity in feet/second,
- $$ y_0 $$ is the initial height in feet,
- The coefficient $$-16$$ accounts for the acceleration due to gravity ($$-32$$ feet/second²) divided by 2.

**For Tara's Ball:**
- Initial height, $$ y_0 = 3 $$ feet,
- Initial upward velocity, $$ v_0 = 12 $$ feet/second.

Thus, Tara's equation is:
$$
y = -16x^2 + 12x + 3
$$

**For Mallory's Ball:**
- Initial height, $$ y_0 = 3.25 $$ feet,
- Initial upward velocity, $$ v_0 = 9 $$ feet/second.

Thus, Mallory's equation is:
$$
y = -16x^2 + 9x + 3.25
$$

Among the provided options, **Option A** accurately represents these equations.

**Answer:**  
A

#### Option A
$$
y=-16 x^{2}+12 x+3
$$
$$
y=-16 x^{2}+9 x+3.25
$$
The correct system of equations is: $$ y = -16x^2 + 12x + 3 $$ $$ y = -16x^2 + 9x + 3.25 $$ So, the answer is **Option A**.

Real Tutor Solution

Answer

Solution

Extra Insights

Related Questions

Latest Algebra Questions