Motion in a Plane Questions: Height, Distance, Velocity

[pharm89]

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 vertical 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 vertical 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 vertical velocity and resultant velocity?
THanks for the help
Pharm 89

 

[cristo]

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 vertical 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 vertical 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 vertical velocity and resultant velocity?

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

 

[pharm89]

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 vertical velocty...would that be the same answer though??
vertical distance = 10 m/15 seconds = 0.666m/s

 

[cristo]

Thanks for your help. So therefore for part c they are asking for the average vertical velocty...would that be the same answer though??
vertical 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!

 

[pharm89]

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...vertical distance = 9.06 m/15 seconds = 0. 6 m/s
Thanks for the assistance.
Pharm 89

 

[MadScientist 1000]

10m? Wasn't it supposed to be 100m?

I took

$$<br /> sin(25)*100m=40m<br />$$

$$<br /> cos(25)*100m=90m<br />$$

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...

$$<br /> 40m/15s = 3 m/s<br />$$

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.

 

[Hootenanny]

A 100m ladder

 

[radou]

$$<br /> sin(25)*100m=40m<br />$$

There is no reason to round off 100*sin(25) = 42.26 to 40.

 

[cristo]

10m? Wasn't it supposed to be 100m?

I took

$$<br /> sin(25)*100m=40m<br />$$

$$<br /> cos(25)*100m=90m<br />$$

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...

$$<br /> 40m/15s = 3 m/s<br />$$

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!

 

[DaveC426913]

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?