Using an angle and time to find Acceleration

[swede5670]

Homework Statement

Jean, who likes physics experiments, dangles her watch from a thin piece of string while the jetliner she is in takes off from Dulles Airport. She notices that the string makes an angle of 21° with respect to the vertical while the aircraft accelerates for takeoff, which takes about 16 seconds. Estimate the takeoff speed of the aircraft.

Homework Equations

Fnet=ma

The Attempt at a Solution

In my class we've just been these problems with 2 variables and I'm confused about finding the first part of the problem so that I can do the later half. I know that since I have time I'm trying to find acceleration or velocity but I don't know where to begin.

 

[LowlyPion]

Homework Statement

Jean, who likes physics experiments, dangles her watch from a thin piece of string while the jetliner she is in takes off from Dulles Airport. She notices that the string makes an angle of 21° with respect to the vertical while the aircraft accelerates for takeoff, which takes about 16 seconds. Estimate the takeoff speed of the aircraft.

Homework Equations

Fnet=ma

The Attempt at a Solution

In my class we've just been these problems with 2 variables and I'm confused about finding the first part of the problem so that I can do the later half. I know that since I have time I'm trying to find acceleration or velocity but I don't know where to begin.

Acceleration can be treated as a vector like velocity.

In your dangling case then there are 2 components. 1) the vertical acceleration of gravity. And 2) the horizontal acceleration moving the watch at an angle.

If you know what the vertical component is (g), and you know the angle 21°, then I trust you know enough geometry to figure out what the horizontal acceleration is and then using acceleration and time to figure out what speed it accelerated to in 16 seconds.

 

[swede5670]

So when I use acceleration as a vector does g just equal the acceleration of gravity or 9.81?
In that case I'm going to first solve for cosine like this:
9.81/X = Cosine (21)
9.81/Cosine(21) = -17.910 m/s/s
Should I have a negative here?

 

[swede5670]

If that is correct then my acceleration is -17.910 m/s^2
Do i convert this to a velocity by multiplying by the 16 seconds? So my speed is 286 m/s?
I just submitted this online and evidently that's wrong. What did I do wrong?

 

[LowlyPion]

So when I use acceleration as a vector does g just equal the acceleration of gravity or 9.81?
In that case I'm going to first solve for cosine like this:
9.81/X = Cosine (21)
9.81/Cosine(21) = -17.910 m/s/s
Should I have a negative here?

First of all you want to use degrees °, not radians. There goes your negative number.

Second of all you might want to use Tangent 21°
because if you draw things out you will see that a/g = tan21° => a = tan 21° * g

 

[swede5670]

Alright so tan (21) * 9.81 = 3.7657 m/s^2
then multiply by 16 to get my velocity?

 

[LowlyPion]

Alright so tan (21) * 9.81 = 3.7657 m/s^2
then multiply by 16 to get my velocity?

Looks about right.

That comes to something like 60m/s or roughly 135 mph.