the first equation in the system models the height, h, of a falling volleyball as a function of time, t. the…

the first equation in the system models the height, h, of a falling volleyball as a function of time, t. the second equation models the height, h, of the hands of a player jumping up to spike the ball as a function of time, t. which statement describes the situation modeled by this system?\n\\begin{cases} h = 14 - 16t^2 \\\\ h = 7 + 24t - 16t^2 \\end{cases}\n\\bigcirc the volleyball is 7 feet above the ground at the instant the player begins her jump.\n\\bigcirc the volleyball is 14 feet above the ground at the instant the player begins her jump.\n\\bigcirc the volleyball is 16 feet above the ground at the instant the player begins her jump.\n\\bigcirc the volleyball is 24 feet above the ground at the instant the player begins her jump.

the first equation in the system models the height, h, of a falling volleyball as a function of time, t. the second equation models the height, h, of the hands of a player jumping up to spike the ball as a function of time, t. which statement describes the situation modeled by this system?\n\\begin{cases} h = 14 - 16t^2 \\\\ h = 7 + 24t - 16t^2 \\end{cases}\n\\bigcirc the volleyball is 7 feet above the ground at the instant the player begins her jump.\n\\bigcirc the volleyball is 14 feet above the ground at the instant the player begins her jump.\n\\bigcirc the volleyball is 16 feet above the ground at the instant the player begins her jump.\n\\bigcirc the volleyball is 24 feet above the ground at the instant the player begins her jump.

Answer

Brief Explanations:

To determine the height of the volleyball when the player starts jumping (at ( t = 0 )), we substitute ( t = 0 ) into the first equation ( h = 14 - 16t^2 ). Plugging in ( t = 0 ), we get ( h = 14 - 16(0)^2 = 14 ). Wait, no—wait, the second equation is ( h = 7 + 24t - 16t^2 )? Wait, no, looking at the system: first equation ( h = 14 - 16t^2 ) (falling volleyball), second equation ( h = 7 + 24t - 16t^2 ) (player's hands). Wait, no, the user's image: first equation ( h = 14 - 16t^2 ), second ( h = 7 + 24t - 16t^2 )? Wait, no, the options: when ( t = 0 ) (start of jump), for the volleyball's height (first equation), ( h = 14 - 0 = 14 )? No, wait, maybe I misread. Wait, the first equation is the volleyball's height: ( h = 14 - 16t^2 ). At ( t = 0 ) (instant player begins jump), ( h = 14 ). Wait, but the options: "The volleyball is 14 feet above the ground at the instant the player begins her jump"—wait, let's check again. Wait, the first equation: ( h = 14 - 16t^2 ) (falling volleyball). When ( t = 0 ) (time when player starts jumping), the volleyball's height is ( 14 - 0 = 14 ). So the correct statement is "The volleyball is 14 feet above the ground at the instant the player begins her jump." Wait, but let's confirm: at ( t = 0 ), substitute into the first equation (volleyball's height function). So ( t = 0 ), ( h = 14 - 16(0)^2 = 14 ). So that's the height of the volleyball when the player starts jumping.

Answer:

The volleyball is 14 feet above the ground at the instant the player begins her jump. (Assuming the first equation is ( h = 14 - 16t^2 ) for the volleyball's height, and ( t = 0 ) is when the player starts jumping. Substituting ( t = 0 ) gives ( h = 14 ).)