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Laurie throws a tennis ball toward her dog from a height of 4.5 ft. The initial vertical velocity of the ball is 18 ft/s. At the same time as Laurie throws the ball, her dog jumps with an initial vertical velocity of 21 ft/s. When the dog jumps, its mouth is 1.5 ft above the ground.

Projectile motion formula:

h = -16t2 + vt + h0

t = time, in seconds, since the ball was thrown

h = height, in feet, above the ground

Which system models the height of the tennis ball and the height of the dog's mouth over time?

h = 4.5t + 18 and h = -16t2 + 1.5t + 21

h = 18t + 4.5 and h =-16t2 + 21t + 1.5

h = -16t2 + 4.5t + 18 and h = -16t2 + 1.5t + 14

h = -16t2 + 18t + 4.5 and h = -16t2 + 21t + 1.5

Respuesta :

Using quadratic function concepts, it is found that the system that models the height of the tennis ball and the height of the dog's mouth over time is given by:

h(t) = -16t² + 18t + 4.5 and h(t) = -16t² + 21t + 1.5.

What is the quadratic function for the height of a projectile?

It is given by:

h(t) = -16t² + v(0)t + h(0)

In which:

  • v(0) is the initial velocity.
  • h(0) is the initial height.

For the tennis ball, we have that v(0) = 18, h(0) = 4.5, hence the equation is:

h(t) = -16t² + 18t + 4.5.

For the dog jump, we have that v(0) = 21, h(0) = 1.5, hence:

h(t) = -16t² + 21t + 1.5.

Hence, the system is given by:

h(t) = -16t² + 18t + 4.5 and h(t) = -16t² + 21t + 1.5.

More can be learned about quadratic function concepts at https://brainly.com/question/24737967

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Answer:

D) h = -16t2 + 18t + 4.5 and h = -16t2 + 21t + 1.5

Step-by-step explanation:

The next answer is, "the time at which the ball and the dog's mouth are at the same height"

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