Vector Calculations for Pilot and Hobo Travel

[blondie26]

vectors! please help no comprendo!

a pilot wishes to fly to a point 450 km due south in 3 hours. A wind is blowing from the west at 50 km/hr. draw the situation and then compute the proper heading and speed the pilot must choose to achieve this objective.

and

a hobo hops a freight car 15m long and 3.0 m wide, the car is moving east 2.5 m/s. exploring the surroundings, the hobo walks from the southeast corner of the car to the southwest corner of the car in 20.0s; then from the south west corner to the northwest corner in 5.0s. with the aid of a vector diagram, compute the hobo's displacement relative to the ground remember the cart is moving as the hobo is walking AND you can only add vectors of the same kind of measurement

please help...i have my final in a couple days and i don't understand this!

 

[Astronuc]

To stay on a straight line south, the pilot must point his plane such the component of lateral component of velocity negates the wind. So if the wind is blowing 'from' west, then the plane must have a velocity component toward the west. Determine the plane's velocity southward, and add the velocity component toward the west to determine the planes resultant velocity.

For the hobo, one can compute the displacement vectors. The train is traveling east at 2.5 m/s, so in 25 seconds how far does it travel?

or one can break into two parts of 20 s and 5 sec.

The 15 m is in the east-west direction.

 

[blondie26]

so for the first one is the answer 200 km/hr and the second one 62m? i totally understand the first one and for the second one i understnad multiplying the velocity by the total change in time so thanx! BUT what i don't understnad is how the problem would be setup/solved differently should the time components be separated...i was just curious...i think that the first way is the easiest but i still want to know how to do the problem using the time components separately...thank u

 

[lightgrav]

No, and no. ... Draw these and you'll see.

For the plane, the plane's motion relative to the air plus the air's motion relative to the ground add up (vectors add tail to tip) to
the plane's velocity relative to the ground , which is directly South.

the hobo displacement (rel.to.car) + car displacement (rel.to.ground) =
hobo displacement (rel.to.ground), which you want to know.
Can you figure out what the first displacements are? [use East = +x]

 

[blondie26]

so obviously i didnt understand! hahaha ok i don't know if this is right either but are u solving for the hypotenuse? if u are then the plane's velocity is 150km/hr + 50km/hr both quantities squared = 25000 then the square root of that is like 158 and with sig figs 160km/hr...or do u have the hyp. as 150 km/hr and one side as 50 km/hr in which case the answer would be 140km/hr or like 100km/hr with sig figs... sry i am sooo stupid and i am still trying to figure out the second one but am i anywhere near the right answer for the first one? god i suck at physics!

 

[lightgrav]

Do you know which way the wind blows?
The plane's velocity (rel.to ground) is perp to this , known.
So these form two legs of a right triangle - the diagonal heading is unknown.

Think of it in two steps : first, the plane flies along some diagonal thru the air,
then, add in the wind across the ground.

 

[blondie26]

yes...the wind is blowing west...so then the answer is 160 km/hr like the first scenario...maybe?

 

[blondie26]

ok the car displacement is 62m because 2.5 m/s times 25 s and then the hobo displacement is maybe possibly either 16m or 18m so the answer could be unless i am totally wrong which of course is probable, between 78m and 80m

 

[lightgrav]

plane 160, okay.

Did you draw this hobo's path with arrows that show direction?
Is the hobo going the same direction as the car? or opposite?

 

[blondie26]

thank u sooo much i am starting to actually get this...thanx for helping me through it...o wait one last question about the plane one it goes 160km/hr and umm the direction it would have to travel is northeast right? or is it east of north...i always get confused and yes...the hobo is moving opposite the car

 

[lightgrav]

actually, your first post says the wind is blowing "From the West",
which must mean "toward the East". So to compensate, the plane heads West of South ... (he's trying to go SOUTH).

The angle "West of South" of the plane heading is found from trig.
sin(theta) = opp/hyp . . . or . . . tan(theta) = opp/adj ; the units cancel.

 

[blondie26]

hahaha ok wow...im really bad at physics...anyway about the hobo...he is moving in an opposite direction which the vector diagram shows but because each value is squared direction will always be postive...so in terms of displacement for the hobo its 16m which means that his displacement relative to the ground is 62m +16m so 78m?

 

[lightgrav]

No, the hobo moves -15 m East + 3 m North , the car moves +62.5 m East.
Are you telling me that East is the same direction as West?
The total displacement (rel.to.ground) is (62.5 - 15) m East + 3 m North.
NOW use Pythagoras.

 

[blondie26]

thank u sooo much...i knew that 15m was negative but i did not know that you had to add it to the car's velocity before using pythagoras...i thought u used pythagoras then added that quantity to the car's velocity...thanx for clearing that up...the directions make soo much more sense now! so with all that said the hobo's displacement is 47m...thank u sooo much for your patience in helping me! ur the best!

 

[lightgrav]

You add normally (keeping track of signs, of course) if they're parallel;
only use Pythagoras at the very end, after each direction (perp.side) is known.

 

[blondie26]

thank u sooooo much! u have no idea well u prob do but how much u've helped me! i luv u! i seriously cannot say thank you enough! :) :)