Answer:
9 years ( approximately)
Step-by-step explanation:
900(1.03)^t = 1200
(1.03)^t= 1.33
( 1.03)^t= ( 1.03)^9
So, t= 9
vi is going in the positive direction (up). (That's my choice). a (acceleration) is going in the minus direction (down). The directions could be reversed.
Givens
vi = 160 ft/s
vf = 0 (the rocket stops at the maximum height.)
a = - 9.81 m/s
t = ????
Remark
YOu have 4 parameters between the givens and what you want to solve. Only 1 equation will relate those 4. Always always list your givens with these problems so you can pick the right equation.
Equation
a = (vf - vi)/t
Solve
- 32 = (0 - 160)/t Multiply both sides by t
-32 * t = - 160 Divide by -32
t = - 160/-32
t = 5
You will also need to solve for the height to answer part B
t = 5
vi = 160 m/s
a = - 32
d = ???
d = vi*t + 1/2 a t^2
d = 160*5 + 1/2 * - 32 * 5^2
d = 800 - 400
d = 400 feet
Part B
You are at the maximum height. vi is 0 this time because you are starting to descend.
vi = 0
a = 32 m/s^2
d = 400 feet
t = ??
formula
d = vi*t + 1/2 a t^2
400 = 0 + 1/2 * 32 * t^2
400 = 16 * t^2
400/16 = t^2
t^2 = 25
t = 5 sec
The free fall takes the same amount of time to come down as it did to go up. Sort of an amazing result.
Each time you are subtracting 1/9 to get the next term
For example, going from term 2 to term 3 is a difference of -1/9
(1 8/9) - (1/9) = 1 7/9
which is why the answer is choice A
Answer:
y = 5/6x - 5.167
Or
y = 5/6x - 31/6
Step-by-step explanation:
The equation of a line
y = mx + c
Step 1: find the slope
m = y2 - y1 / x2 - x1
Given points
( 0 , -7) ( 5 , -1)
x1 = 0
y1 = -7
x2 = 5
y2 = -1
Insert the values into the equation
m = -1 - (-7) / 5 - 0
m = -1 + 7 / 5
m = 6/5
y = 6/5x + c
Step 2: sub any of the two points given into the equation
y = 5/6x + c
( 5 , -1)
x = 5
y = -1
-1 = 5/6(5) + c
-1 = 5*5/6 + c
-1 = 25/6 + c.
c = -1 - 25/6
LCM = 6
c = -6 - 25 / 6
c = -31/6
c = -5.167
Step 3: sub c into the equation
y = 5/6x + c
y = 5/6x - 31/6
Or
y = 5/6x - 5.167
The equation of the line is
y = 5/6x - 5.167
