Answer:
a. h(t) = -16t^2 +12t + 4.
b. 5.04 ft
c. 6 ft.
d. 1 second.
Step-by-step explanation:
a.
This is upward motion against the force of gravity. The acceleration due to gravity is 32 ft s-2.
An equation modelling this is
h(t) = ut + 1/2 gt^2 + 4 where h(t) = height of the birdie at time t, g = acceleration due to gravity, t = the time and u = the initial velocity.
u = 12 and g = -32 (because the flight is against gravity) so we have:
h(t) = 1/2 * -32 t^2 + 12t + 4
h(t) = -16t^2 + 12t + 4
b. At t = 0.1 seconds the height is 12(0.1) - 16(0.1)^2 + 4
= 1.2 - 0.16 + 4
= 5.04 ft.
c. At t = 0.25 the height is 12(0.25) - 16(0.25)^2 + 4
= 6 feet
d . When the birdie reaches the ground h will be 0 so
12t - 16t^2 + 4 = 0
-4t^2 + 3t + 1 = 0
(4t- 1)(-t - 1) = 0
t = -0.25, t = 1
t = 1 ( ignore the negative root).
t = 1 second.
