Aball is projected upward at time t = 0.0 s from a point on a roof 90 m above the ground. the ball rises, then falls and strikes the ground. the initial velocity of the ball is 80.5 m/s. the velocity of the ball when it is 89 m above the ground is about :

17.

Remark: This has a trick in it. (They all do). The question asks about a speed below the starting point (which is 90 meters above the ground level and you are asking what happens at 89 meters, the distance is actually - 1 meters (remember I always take down to be minus.)

Givens

d = - 1

a = - 9.81

vi = 80.5 upwards (positive)

vf = ??

Equation

vf^2 = vi^2 + 2*a*d

vf^2 = 80.5^2 + 2*(-9.81)(-1)

vf^2 = 6480.25 + 19.62

vf = - sqrt(6499.82) You are going down remember.

vf = - 80.62

18

Remark: I had help from @Mathmate who told me that what I was overlooking the fact that vi is zero. I've watched hundreds of NASA Rocket launches and I would never in a million thought of the initial velocity being zero, but it is. Think back to any launch you have ever seen. Don't they start at zero?

Givens

vi = 0

vf = 40 m/s

d = 97

a =

Equation

vf^2 = vi^2 + 2*a*d

Solve

40^2 = 0 + 2 * a * 97)

1600 = 194a

a = 1600 / 194

a = 8.25

Note a 5 is always hard to handle in rounding. Apparently the rule for you is don't. Anyway it is going up.

19

Givens

Remark Remember up is plus, down is minus.

vi = 30

a = - 1.62

d = 180 which I assume is up.

Comment: This is one of the nastiest questions you could get if you have never seen it before. Almost everyone I know has to be taught how to do it the first time. Here's what the problem is. If you try to find t directly you are going to have to use

d = vi*t + 1/2at^2

You could do that, but the trouble is that you get 2 values for t and it is very hard to decide which is correct. The two values are t = 7.53 and 29.02. On the strength of rounding, you could pick 30, but then the question would have 2 answers and that is not possible.

What to do you ask? This is one of the very few times you will have to solve for vf becore you can solve for t

Equation

vi = 30 m/s

a = - 1.62 m/s^2

d = 180 (up)

vf = ???

vf^2 = vi^2 + 2*a*d

vf^2 = 30^2 + 2(-1.62)(180)

vf^2 = 316.8 which I take to be ascending

vf = 17.79 m/s

I'm going to let you complete the problem.

Equation

a = (vf - vi)/t

You have vi vf and a (remember a is minus). Solve for t. This part should be easy.

20

Remark. This little piece of work depends on "what goes up must come down." And at the same speed it went up.

Givens

vi = 41

vf = -41

a = - 9.81

t =

Equation

a = (vf - vi)/t

Solve

-9.81 = (-41 - 41) / t

t = - 82/- 9.81

t = 8.359 which they make as 8.4. This set of exercies is inconsistent about what to do with a 5 when rounding. Anyway, I am done.

(x, y)→(x − 8, y − 7)

step-by-step explanation:

enjoy!

x ≥ 18 is your answer

step-by-step explanation:

let "a number" = x

(2/3)x + 17 ≥ 29

isolate the variable (x). do the opposite of pemdas (parenthesis, exponent (& root), multiplication, division, addition, subtraction).

first, subtract 17 from both sides.

(2/3)x + 17 (-17) ≥ 29 (-17)

(2/3)x ≥ 29 - 17

(2/3)x ≥ 12

next, multiply 3/2 to both sides to isolate the x

(3/2)(2/3)x ≥ 12(3/2)

x ≥ 12(3/2)

simplify. multiply, then divide

x ≥ (12 * 3)/2

x ≥ (36)/2

x ≥ 18

x ≥ 18 is your answer

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