50 points 1. a model rocket is launched from the ground with an initial velocity of 160 feet/sec. a. how long will it take the rocket to reach its maximum height? b. assume the model rocket’s parachute failed to deploy and the rocket fell back to the ground. how long would it take the rocket to return to earth from the time it was launched? show all work in the space provided.

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.

(0,-3) see attached graph

step-by-step explanation:

a. to solve the system, graph the two equations.

x = y+3 becomes y=x-3 has m=1/1 and b=-3. start at (0,-3) on the y-axis and plot a point. then move up 1 unit and 1 unit to the right. plot a point and connect.

y=-4x+3 has m =-4/1 and b=-3. start at (0,-3) on the y-axis and plot a point. then move down four units and to the right 1 unit. plot a point and connect.

the solution is the point (x,y) where the two lines intersect. by the graph below it is (0,-3).

b. to solve by substitution, substitute y = -4x-3 into x= y+3

x= (-4x-3) +3

x=-4x

5x=0

x=0

now substitute x = 0 back in to find y.

y= -4(0)-3

y=0-3

y=-3

solution is (0,-3)

c. use elimination by adding the equations together.

x-y=3

4x+y=-3

5x=0

x=0

then substitute into one equation to find y.

y=-4(0)-3

y=-3

i think there was a typo. you wrote pat brings 3 quarts of ice-cream to the party. each serving of ice-cream is 1 6 quart. how many total servings of ice-cream does pat bring to the party? i think the bold is supposed to be 1/6. so 1 quart of ice cream = 6 servings. 6 * 3 = 18.