Motion in a Plane Questions: Height, Distance, Velocity

At first I wondered why he shrunk the ladder from 100m to 10m in his calcs. But 10m has to be the correct size. Can you imagine climbing 100m in 15s?In summary, the conversation discusses a problem involving a firefighter climbing a 100 m ladder against a vertical wall at an angle of 25 degrees. The questions ask for the height of the wall, the distance of the base of the ladder from the wall, and the firefighter's average vertical velocity. The solution involves using the Pythagorean Theorem and the formula for velocity, resulting in a height of 9.06 m, a distance of 4.2 m, and an average vertical velocity of
  • #1
pharm89
32
0

Homework Statement



Hi, I have some answers to the following questions but I would just like to know if I am understanding the concepts correctly.

A firefighter climbs up a 100 m ladder leaning against a verticle wall. The ladder makes an angle of 25 degrees with the wal. The firefighter reaches th eroof in 15 seconds.
(a) what is the height of the wall?
(b) how far is the base of the ladder from the wall?
(c) what is the firefighters average verticle velocity?

Homework Equations


Pythagorean Theorum - (a^2) + (b^2) = c^2
velocity (v) = distance/time


The Attempt at a Solution



(a) COS = adjacent/hypotenuse
Cos25 degrees = X/10 m
0.91 = x/10m
X= 9.06 m

(b) a^2 +b^2 = c^2
a^2 + (9.06)^2 = 10^2
a^2 +82.08 = 100
a^2 = 17.92
a= 4.2 m

(c) given distance up ladder = 10 m
time = 15.0 seconds
Required: velocity
Analysis: velocity = distance/time =10m/15s = 0.666 m/s

what is the difference between average verticle velocity and resultant velocity?
THanks for the help
Pharm 89
 
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  • #2
pharm89 said:

Homework Statement



Hi, I have some answers to the following questions but I would just like to know if I am understanding the concepts correctly.

A firefighter climbs up a 100 m ladder leaning against a verticle wall. The ladder makes an angle of 25 degrees with the wal. The firefighter reaches th eroof in 15 seconds.
(a) what is the height of the wall?
(b) how far is the base of the ladder from the wall?
(c) what is the firefighters average verticle velocity?

Since you've used 10m in your calculations, I presume this is a typo.

The Attempt at a Solution



(a) COS = adjacent/hypotenuse
Cos25 degrees = X/10 m
0.91 = x/10m
X= 9.06 m
Method correct.. I don't have a calculator to check your maths though. Also, this is correct, if we make the asumption that the ladder reaches the very top of the building, which we must make here.

(b) a^2 +b^2 = c^2
a^2 + (9.06)^2 = 10^2
a^2 +82.08 = 100
a^2 = 17.92
a= 4.2 m
Again, correct method

(c) given distance up ladder = 10 m
time = 15.0 seconds
Required: velocity
Analysis: velocity = distance/time =10m/15s = 0.666 m/s

what is the difference between average verticle velocity and resultant velocity?

You have calculated the resultant velocity. The vertical velocity will be v=(vertical distance)/(time)
 
  • #3
cristo said:
Since you've used 10m in your calculations, I presume this is a typo.

Method correct.. I don't have a calculator to check your maths though. Also, this is correct, if we make the asumption that the ladder reaches the very top of the building, which we must make here.


Again, correct method



You have calculated the resultant velocity. The vertical velocity will be v=(vertical distance)/(time)

Thanks for your help. So therefore for part c they are asking for the average verticle velocty...would that be the same answer though??
verticle distance = 10 m/15 seconds = 0.666m/s
 
  • #4
pharm89 said:
Thanks for your help. So therefore for part c they are asking for the average verticle velocty...would that be the same answer though??
verticle distance = 10 m/15 seconds = 0.666m/s

No, the vertical distance is what you calculated in (a) i.e. the height of the building. Draw a diagram, you'll see that the length of the ladder, 10m, is not a vertical distance!
 
  • #5
cristo said:
No, the vertical distance is what you calculated in (a) i.e. the height of the building. Draw a diagram, you'll see that the length of the ladder, 10m, is not a vertical distance!

Yes, that makes sense...verticle distance = 9.06 m/15 seconds = 0. 6 m/s
Thanks for the assistance.
Pharm 89
 
  • #6
10m? Wasn't it supposed to be 100m?

I took

[tex]

sin(25)*100m=40m

[/tex]

[tex]

cos(25)*100m=90m

[/tex]

Instead of doing it the hard way without going through Pythogarous and keeping the idea of significant digits in my head.

And no tough work involved here...

[tex]

40m/15s = 3 m/s

[/tex]

Got 3 m/s, which isn't the same as you'lls (The Texan accent triumphs again)

But pharm89, where did the 10m instead of the 100m come from?

Please be careful in calculations.
 
Last edited:
  • #7
:bugeye: A 100m ladder :bugeye:
 
  • #8
MadScientist 1000 said:
[tex]

sin(25)*100m=40m

[/tex]

There is no reason to round off 100*sin(25) = 42.26 to 40.
 
  • #9
MadScientist 1000 said:
10m? Wasn't it supposed to be 100m?

I took

[tex]

sin(25)*100m=40m

[/tex]

[tex]

cos(25)*100m=90m

[/tex]

Instead of doing it the hard way without going through Pythogarous and keeping the idea of significant digits in my head.

And no tough work involved here...

[tex]

40m/15s = 3 m/s

[/tex]

Got 3 m/s, which isn't the same as you'lls (The Texan accent triumphs again)

But pharm89, where did the 10m instead of the 100m come from?

Please be careful in calculations.

I presumed (and was apparently right, as the poster didn't correct me) that there was a typo in the original post, and it should in fact be 10m. And, as Hootenanny points out, 100m is a little long for a ladder!
 
  • #10
At first I wondered why he shrunk the ladder from 100m to 10m in his calcs.

But 10m has to be the correct size. Can you imagine climbing 100m in 15s?
 

1. What is the difference between distance and displacement?

Distance refers to the total length covered by an object in a given time, while displacement refers to the straight-line distance between the initial and final position of an object.

2. How is velocity calculated in motion in a plane?

Velocity in motion in a plane is calculated by dividing the displacement of an object by the time taken for that displacement.

3. What is the difference between average velocity and instantaneous velocity?

Average velocity is calculated over a specific period of time, while instantaneous velocity refers to the velocity at a particular moment in time. Average velocity is the total displacement divided by the total time, while instantaneous velocity is the derivative of the position function with respect to time.

4. How does angle of elevation impact the height and distance traveled by an object?

The angle of elevation affects the height and distance traveled by an object because it determines the vertical and horizontal components of the object's velocity. The greater the angle of elevation, the higher the object will travel and the farther it will travel horizontally.

5. How does air resistance affect the motion of an object in a plane?

Air resistance, or drag, is a force that opposes the motion of an object in a plane. It can slow down the object and change its trajectory, making it travel a shorter distance and at a slower speed than if there was no air resistance. The effect of air resistance is more prominent for objects with larger surface areas and lower densities.

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