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Sagot :
y(initial) = 9
V(initial) = 168
V(final) = 0
g(accel-grav) = 32 (in feet per second
squared)
Use the following equation:
V(final) = V(initial) + a(t)
Since this object is moving straight up and
down, a = -32
Enter the knowns into the equation
0 = 168 - 32t
32t = 168
t = 168/9.8
t = 5.25
Now that you know the time it takes to
reach it's maximum, use the general
kinematics equation to solve for final
distance:
y(final) = y(initial) + V(initial)(t) + (1/2)a
(t²)
y(final) = 9 + 168(5.25) + (1/2)(-32)
(5.25²)
= 9 + 882 - 441
= 450 feet
V(initial) = 168
V(final) = 0
g(accel-grav) = 32 (in feet per second
squared)
Use the following equation:
V(final) = V(initial) + a(t)
Since this object is moving straight up and
down, a = -32
Enter the knowns into the equation
0 = 168 - 32t
32t = 168
t = 168/9.8
t = 5.25
Now that you know the time it takes to
reach it's maximum, use the general
kinematics equation to solve for final
distance:
y(final) = y(initial) + V(initial)(t) + (1/2)a
(t²)
y(final) = 9 + 168(5.25) + (1/2)(-32)
(5.25²)
= 9 + 882 - 441
= 450 feet
The maximum or minimum of a function is the point
where its first derivative = 0.
h(t) = -16t² + 168t + 9
First derivative h'(t) = -32t + 168
h'(t) = 0 = -32t + 168 = 0
Add 32t to each side: 32t = 168
Divide each side by 32: t = 5.25 seconds
h(t) = -16t² + 168t + 9
Height at 5.25 seconds = -16(5.25²) + 168(5.25) + 9 =
-16(27.5625) + 882 + 9 =
- 441 + 882 + 9 = 450-ft
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