Henry is standing on a bridge over a creek. If he could throw a stone straight up into the air with a velocity of 50 feet per second, could the stone reach a height of 60 feet above the creek? He is 20 feet from the water

Answers

Answer 1

Answer: Henry is 20 feet above the water. You want to know whether stone can reach
60 feet above the water. So what you're really asking is: Calculate whether
the stone can reach 40 feet above Henry, and we can forget about the creek ?

Call Henry's elevation zero, and the height of the stone at any time after
the toss 'H'.

Way back among the pages in your Physics book that are clean and shiny
because they have never yet been exposed to air or sunlight, you will find
the formula for the height of an object in free-fall:

Height = H₀ + V₀t + 1/2 A t²

H₀ = the object's height when it was released
V₀ = the object's speed when it was released, negtive if downward
A = the object's acceleration, negative if downward
t = time since the object was released

In the case that involves Henry on the bridge . . .

H₀ = 0
V₀ = +50 ft/sec
A = -32 ft/sec² (acceleration due to gravity)

We want to know if the height of the object can ever be +40 feet.
We can plug all the numbers into the equation, and solve it. Since the equation
is written in terms of ' t ', any solution we get will be a 'time'. That's not what
we're looking for, but if there's any real solution, then we'll know that it's possible.

40 = 50t + 16t²

Subtract 40 from each side:

16t² + 50t - 40 = 0

Just to make the numbers more manageable, divide each side by 2 :

8t² + 25t - 20 = 0

Plug this into the quadratic formula:

t = (1/16) x (-25 plus or minus the square root of [625 - 640] )

Do you see that 'square root of -15 in there ?

The ' -15 ' is called the 'discriminant' of our quadratic equation, and
since it's negative, our equation has no real solutions ... there's no
such thing as the real square root of a negative number.

So the answer to the question is: No. The stone never reaches a height
of 40 feet above Henry, or 60 feet above the creek.

Whew!
===============================================

A slightly easier way to do it:

Henry throws the stone upward at 50 ft/sec.
The acceleration of gravity is 32 ft/sec² downward.

The stone keeps rising for (50/32) = 1.5625 second, until its upward speed
has shrunk to zero, and then it starts falling.

How high is it when it stops rising ?

Its upward speed was 50 when Henry tossed it, and zero when it stopped rising.
Its average speed on the way up was (1/2)(50 + 0) = 25 ft/sec upward.

It has that average speed for 1.5625 seconds.
How far does it climb in that time ?

H = (25 ft/sec) x (1.5625 sec) = 39.0625 feet.

That's pretty close, but not quite 40 feet above Henry.
So the answer to the question is: No.

Answer 2

Answer: Balance the energy=
K.E.=P.E(at the max height)
1/2mv^2=mgh
m cancels out,
or, h=1/2v^2/g
or, h=1/2*50*50/32
or, h=39 ft (approx.)
As he is 20 ft above water so total height the stone an reach 39+20=59 ft.
Hence, it can't reach 60 ft over the creek.

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1. Raymond is repairing wires on a radio broadcast tower. He is in a basket of the repair truck40m from the tower. When he looks up, he estimates the angle of elevation to the top of thetower as 42°. When he looks down, he estimates the angle ofdepression to the bottom of the tower as 32°. How high is the towerto the nearest tenth of a metre?

Gloria has a lunch account in the school cafeteria. The balance, f(x), in her account can be represented by the function f(x) = –1.50x + 40, where x is the number of meals purchased. Suppose –1.50 changed to –2.75. What does this mean in the context of the problem?

Answers

f(x) = -1.50x + 40.....basically, this is saying that Gloria has 40 bucks in her lunch account and each meal costs her 1.50.

By changing the -1.50 to -2.75 means she is paying more for her meals...the cost of a meal went up from 1.50 to 2.75.

Final answer:

The change from -1.50 to -2.75 indicates an increase in the cost of the meals. Consequently, Gloria's lunch account balance will deplete faster now.

Explanation:

In the context of this problem, f(x) = –1.50x + 40 represents how much money Gloria has left in her lunch account after purchasing x number of meals. The coefficient of x, -1.50, indicates the cost per meal. If –1.50 changed to –2.75, it would mean that the cost of each meal has increased from $1.50 to $2.75. Consequently, Gloria's account balance would decrease faster, signifying that less meals can now be purchased with the same amount of money.

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Wheels are 1.25 inches in diameter covert the wheels diameter to feet

Answers

Wheels are 1.25 inches in diameter covert the wheels diameter to feet For this process to take place or in order to convert the said measurement to another such as inches to feet, we first have to determine the conversion values for the units asked. Thus,
1. 1 in = 0.0833333 foot

Solution.
a. 1.25 in x 0.0833333 ft / 1 in = 0.1041667 ft

Answer:

0.1041667 (approximation)

Step-by-step explanation:

divide that by 12

Which is longer ; 180 seconds or 3 minutes?

Answers

Both 180 seconds or 3 minutes are equal.

What is division?

The division in mathematics is one kind of operation. In this process, we split the expressions or numbers into the same number of parts.

Given:

We have two times,

180 seconds and 3 minutes.

180 seconds in minutes,

= 180/60

= 3 minutes.

Therefore, both are the same.

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how you find the answer is you divide 60 into 180 and you get 3 which means 3 minutes so their both the same

A barge travels twice as fast when it is empty as when it is full. If it travels 20 miles northwith a cargo, spends 20 minutes unloading, and returns to its original port
empty, taking 8 hours to complete the entire trip, what is the speed of the barge when it
is empty?

Answers

V1=(empty)=2*v2(full)
20+20 (go+return)
t1+t2=8hour-20’(1/3 hour)=23/3hour
t1=23/3-t2
v1*t1+v2*t2=20+20
2v2*(23/3-t2)+v2*t2=40
2v2*23/3-2v2*t2+v2t2=40
2v2*23/3-v2t2=40
2v2*23/3-20=40
2v2*23/3=60
v2=60/46/3=180/46=90/23
v1=2*90/23=180/23

Answer:wada

Step-by-step explanation:

awdasd asd wasd waswd

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Answers

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One hundred thirty people were asked to determine how many cups of fruit and water they consumed per day. The results are shown in the frequency table. Identify the conditional relative frequency by row. Round to the nearest percent. The conditional relative frequency that someone ate more than 2 cups of fruit, given the person drank less than or equal to 4 cups of water is approximately . The conditional relative frequency that someone ate less than or equal to 2 cups of fruit, given the person drank more than 4 cups of water is approximately .

Answers

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Step-by-step explanation:

Answer:

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Step-by-step explanation:

i did it on egdenuity

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