A plane is flying through the air at a velocity 88km/hr

In summary, the plane has travelled a total distance of 74.99km, with 73.04km being in an easterly direction and 60.96km in a northerly direction. The plane's position can be found by using vector addition to add the displacement due to the engine and the displacement due to the wind.
  • #1
jacknjersey
13
0

Homework Statement



A plane is flying through the air at a velocity 88km/hr direction N37'E on a day when there is no wind.
a) After 50 minutes, how far has the plane gone?
b) How far east is it from it's starting point?
c) How far north is it from its starting point?

If there is a wind blowing FROM due south at 17mk/hour, what would be the answers to the question above?

Homework Equations




time=distance/speed

The Attempt at a Solution



50 minutes = distance/ 88 km/h
 
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  • #2
welcome to pf!

hi jacknjersey! welcome to pf! :smile:
jacknjersey said:
time=distance/speed

50 minutes = distance/ 88 km/h

ok, now convert minutes to hours …

(you need everything to be in the same units! :wink:)

the distance is … ? :smile:

(time=distance/speed, speed=distance/time, distance=speed*time)
 
  • #3


50 minutes is 0.83 hours

so now I have distance = speed x time

distance = 0.83 x 88
73.04km

I'm not sure what to use to get b and c - how far north and east? argh.
 
  • #4
jacknjersey said:
I'm not sure what to use to get b and c - how far north and east? argh.

well, you know the angle (37° to the right of north) …

so draw a triangle, and use cos and sin :wink:
 
  • #5


you rock. tx!
 
  • #6


cos theta = adjacent/ hypotenuse
cos 37'=x/ 73.04
x=55.90584235
x=55.91km

sin theta = opposite/hypotenuse
sin 37'= y/73.04
y=73.04 sin 37
y=43.96km

If the wind was blwoing from the south at 17km/hour, the wind is blowing due north.

therefore:

after 50 minutes at 17 km p/h, plane has travelled
distance = 0.83 x 17
distance = 14.11km

how far east is it fromit's starting point?how far north is it from it's starting point?
 
  • #7
you can regard the wind as being separate from the engine …

just ad the displacement due to the wind to the displacement due to the engine :wink:
 
  • #8


simply put, 17+88?
 
  • #9
no!

add the displacements (the changes in position, the distances)
 
  • #10


the plane went 73.04km. add the wind of 17.
= 90.04
 
  • #11
haven't you been taught vector addition?

to add displacements, you have to add the x and y amounts (the components) separately

(try drawing it)
 
  • #12


do i have all the coordinates?
 
  • #13
jacknjersey said:
do i have all the coordinates?

yes!
 
  • #14


Ive done a drawing and to get the resultant vector, i need to draw a tail from the head of the second to the tail of the first and find that length. the length of this vector is the magnitude of the resultant vector.

Should i paste in my picture?
 
  • #15
hi jacknjersey! :smile:
jacknjersey said:
Ive done a drawing and to get the resultant vector, i need to draw a tail from the head of the second to the tail of the first and find that length. the length of this vector is the magnitude of the resultant vector.

that's correct :smile:

but do b) and c) first (how far east and north), then you can use pythagoras to find the magnitude :wink:
 
  • #16


how far east? 73.04
how far north from starting point? 17 + 43.96 = 60.96km
how far has the plan gone? x^2=73.04^2 + 17^2 = 74.99km
 
  • #17
jacknjersey said:
how far north from starting point? 17 + 43.96 = 60.96km

that's right! :smile:
how far east? 73.04

no 73.04 was the total distance from the engine, you need to use the east distance (and add 0 :wink:)
how far has the plan gone? x^2=73.04^2 + 17^2 = 74.99km

no, for the total magnitude, use pythagoras on the total north and total east
 

Related to A plane is flying through the air at a velocity 88km/hr

1. What is the velocity of the plane?

The velocity of the plane is 88km/hr. This is the speed and direction at which the plane is moving through the air.

2. How is velocity different from speed?

Velocity and speed are often used interchangeably, but they have different meanings in physics. Velocity takes into account the direction of motion, while speed only measures the rate of change in position.

3. Is 88km/hr a fast speed for a plane?

This depends on the type of plane and its purpose. For commercial jets, 88km/hr is relatively slow. However, for smaller planes such as propeller planes, this may be considered a moderate speed.

4. What factors can affect the velocity of a plane?

The velocity of a plane can be affected by several factors, including the type and size of the plane, air resistance, wind speed and direction, and the force of the engines.

5. How is the velocity of a plane measured?

The velocity of a plane is typically measured using instruments such as pitot tubes, which measure the difference in air pressure between the front and back of the plane. This information is then used to calculate the velocity of the plane.

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