physics help please?

Question

The speed of an object and the direction in which it moves constitute a vector quantity known as the velocity. An ostrich is running at a speed of 25.6 m/s in a direction of 80° north of west. Please explain how you get the answer.

(a) What is the magnitude of the ostrich's velocity component that is directed due north? (answer in m/s)

(b) What is the magnitude of the ostrich's velocity component that is directed due west? (answer in m/s)

Answer 1

u have to draw it out and draw your north , south , east west cordinates. from the north co-ordinate going west its 80 degree , so draw vector there at an 80 degree angle in betn north west and the magn of tht line is 25.6,
a. north - use the right angle triangle rule draw line from the line end to the north end , u get a right angle triangle , so the angle is 80 , 10 , 90 , therefore sin 10 = magn of north /25.6 and therefore magn of north = sin 10 * 25.6
similarly
b. cos 10 = 25.6/magn of west , therefore magn of west = 25.6/cos 10

Answer 2

First of all for your orientation of direction, 80º north of west means 350º on the complete 360º circle rotating clockwise where W = 270º and add 80º towards N will yield to 350º that is.

Then use the very simple Trigonometric function mnemonic codes SOHCAHTOA to immediately calculate results.

(a) magnitude (due north) = sine 80º x 25.6
= 25.21 m/s
(b) magnitude (due west) = cosine 80º x 25.6
= 4.44 m/s

The above results were now be acceptable, however if you want more accuracy, you have to use the spherical triangles considering that the ostrich runs on the spherical earth but it won't be necessary to be that accurate for the earth is actually an oblate spheroid and not a perfect spheroid, and the distance that the ostrich covers is too small to calculate and economize its fuel for the calorie burning activity.

Answer 3

Draw a right triangle where the hypoteneuse length is 25.6 and the directions of the sides are north and west.

The northern component of the velocity is given by the ratio of the side opposite divided by the hypoteneuse, or the sine of 80 degrees, which is 0.9848. Multiply this by 25.6 to get 25.2 m/s north.

The western component = side adjacent / hypoteneuse = cosine of 80 degrees = 0.1736, so that velocity is 4.45 m/s west.

Check the answers with the Pythagorean formula: (25.6)^2 = (25.2)^2 + (4.45)^2.