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 + 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 + (-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