Mark hits a tennis ball into the air. He uses the equation shown to approximate the height in feet of the ball t seconds after he hits it. What does the 4 represent

Answer 1

In a quadratic equation that models the height of an object in projectile motion, such as a tennis ball, the general form is often represented as:

\[ h(t) = -at^2 + bt + c \]

where:

• \( h(t) \) is the height of the object at time \( t \),
• \( -a \) is a coefficient representing the effect of gravity,
• \( b \) is the initial velocity of the object,
• \( c \) is the initial height from which the object is launched.

If the equation you are referring to is something like \( h(t) = -at^2 + bt + 4 \), then the "4" represents the initial height \( c \) of the ball in feet. This means that at time \( t = 0 \), the ball was at a height of 4 feet, indicating where Mark hit the ball from (perhaps above ground level).

Answer 2

h = -16t^2 + 88t + 4

Answer 3

In the equation you've provided,

\[ h(t) = -16t^2 + 88t + 4, \]

the components represent the following:

• \( h(t) \): the height of the tennis ball in feet at time \( t \) seconds after it has been hit.
• \(-16t^2\): This term represents the effect of gravity (in feet per second squared). This coefficient is typically half of the acceleration due to gravity (which is approximately \( 32 , \text{ft/s}^2 \)).
• \(88t\): This term represents the initial upward velocity of the ball in feet per second. It indicates how fast the ball was moving upward when it was hit.
• \(4\): This constant represents the initial height of the ball when it was hit, measured in feet. So, in this context, the "4" means that Mark hit the ball from a height of 4 feet above the ground.

In summary, the "4" in your equation indicates the initial height of the tennis ball at the moment it was struck by Mark.