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.
The magnitude of WX is 
⇒ c
Step-by-step explanation:
The magnitude of XY (its length) where,
is IXYI = 
∵ W = (-2 , 8 , -3)
∵ X = (1 , 4 , -1)
- To find the magnitude of WX use the formula above
∴ 
= -2 and 
= 1
∴ 
= 8 and 
= 4
∴ 
= -3 and ![z_{2]](https://tex.z-dn.net/?f=z_%7B2%5D)
= -1
- Substitute these values in the rule above
∵ IWXI = 
∴ IWXI =
The magnitude of WX is
Learn more:
You can learn more about the position of an object in brainly.com/question/10940255
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Answer:
(4,0) and (- 2,0): Answer
Step-by-step explanation:
Absolute value questions have two essential steps.
1. Solve the equation as it is written.
2. Solve it changing the sign of the right hand side. I will include a graph to confirm my answer
4*abs(x - 1) = 12 Divide by 4
- abs(x - 1) = 12/4
- abs(x - 1) = 3 Equate this to 3
- x - 1 = 3 Add 1 to both sides
- x - 1 + 1 = 3 + 1 Combine
- x = 4
4*abs(x - 1) = - 12 Divide by 4
- abs(x - 1) = - 12/4
- abs(x - 1) = - 3
- x - 1 = - 3 Add 1 to both sides
- x - 1 + 1 = -3 + 1
- x = - 2
So this has 2 answers
(4,0) and (- 2,0)
A=3 so 8*3=24.......................
The domain is t=0 to t=3.2 and range is y = 0 to 57.125 feet.
<u>What are Domain and range of a Function?</u>
- The range of values that we are permitted to enter into our function is known as the domain of a function.
- The x values for a function like f make up this set (x). A function's range is the collection of values it can take as input.
- After we enter an x value, the function outputs this sequence of values. The y values are those.
- A function can be compared to a piece of equipment on an assembly line.
- A few screws and nuts are located on one end of the assembly line, while a car is located on the other. The function is the device in the center. The domain is the screws and bolts that we insert into the machine. The car at the other can be thought of as the range.
Given function is : y = -16t^2 + 50t + 4
It hits the ground when y=0
0 = -16t^2 + 50t + 4
8t^2 -25t -2 = 0
t = 25/16 + (1/16)sqrt(625+64) = (25+26.25)/16 = 51.25/16 = 3.2 seconds
domain is t=0 to t=3.2 [3.2]
take the derivative and set it equal to zero to find maximum height
-32t +50 = 0
t = 50/32 = 25/16 = 1.5625 seconds
-16(25/16) + 50(25/16) + 4 = 34(25/16) + 64/16 = (17(25)+32)/8 = 57.125 = maximum height
range is y = 0 to 57.125 feet. the discus goes from 4 feet to 57 1/8 feet and back down to 0 feet.
Know more about Domain and Range with the help of the given link:
brainly.com/question/20349151
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