Two Physics Questions?

Question

1.) In a 2-dimensional Cartesian coordinate system the y-component of a given vector is equal to that vector's magnitude multiplied by which trigonometric function, with respect to the angle between vector and y-axis?

The answer is cosine...Why?

2.) A runner circles a track of radius 100 m in 100s moving at a constant rate. If the runner was initially moving north, what has been the runner's average acceleration when halfway around the track?

The answer is: 0.25 m/s^2, south...Why?

Answer 1

Hi.
1) Because the triangle formed by the vector involves the adjacent side / the hypotenuse (vector).
2) The total distance (100 x 2 x pi) or 628.318531 m is covered in 100 seconds. This works out to a velocity of 6.2831...m/s. Acceleration is change is velocity which, for each half of the circle takes 50 seconds. Can you work it out from here?

Answer 2

1) That is the definition of the cosine value of an angle.
2) The net acceleration at that point in time results in the runner moving due south (with the same speed). Since hius velocity changed from due north to due south, then the net acceleration had to be in the south direction.

Answer 3

#1 N 2d (. I ) ?
cosine+ a hunk of matter that is not useful, because people believe numbers vanish when you put two thing like that together

#@2 runnung sirkel

because it was there before you, it worked woth you, and it need not change when you are applyed

Answer 4

because the sum of x is the integer of pi

Answer 5

thats confusing