Because they do not have like bases.
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.
3/8=0.375
2/5=0.4
0.38=0.38
0.375<0.38<0.4
therefore: 3/8,0.38,2/5
*Remember that you can convert fractions to decimals by dividing the numerator by the denominator! This makes it much easier to compare :)
The substitution property of equality, one of the eight properties of equality, states that if x = y, then x can be substituted in for y in any equation, and y can be substituted for x in any equation.
Answer: 4. (-1,-1) 3. (3,-2)
4)
Set the equations equal to each other.
4x+3=-x-2
Subtract 3 from both sides
4x=-x-5
Add x to both sides
5x=-5
Divide both sides by 5
x=-1
Next, replace x with -1 in either equation to find y.
-(-1)-2=y
-1=y
3)
Do the same thing for this one and set them equal to each other
-2x+4=-1/3x-1
Add 1 to both sides
-2x+5=-1/3x
Add 2x to both sides
5=5/3x
Divide both sides by 5/3
x=3
Next, replace x with 3 in either equation
-2(3)+4=y
-2=y
