Question

***please answer***

Answer 1

Answer:

The quadratic function that model the situation is

h(t) = - 16 t² + 68 t + 12

Step-by-step explanation:

The formula of the distance for free fall of an object is h(t) - h(0) = ut + $\frac{1}{2}$ at², where

• h(t) is the height of the object in feet after t seconds
• u is the initial velocity of the object
• a is the acceleration of gravity in feet per second²

Jamie throws a ball into the air with an initial upward velocity of 68 feet per second from a height of 12 feet

∵ The initial velocity is 68 feet/second

∴ u = 68

∵ The initial height is 12 feet

∴ h(0) = 12

- The acceleration of gravity is about - 32 feet/sec² (the direction

    of motion is upward)

∴ h(t) - 12 = 68 t + $\frac{1}{2}$ (-32) t²

- Add 12 to both sides

∴ h(t) = 68 t - 16 t² + 12

- Arrange the terms from greatest power of t

∴ h(t) = - 16 t² + 68 t + 12

The quadratic function that model the situation is

h(t) = - 16 t² + 68 t + 12