Question

A golf ball is whacked in a direction 25 degrees south of the east axis. The ball travels 125m. What are the east and north components of its displacement?​

Answer 1

We are given:

Direction of motion: 25 degrees south of the east axis

Distance covered  = 125 m

East component of the Ball:

this component is denoted by green color in the image

Once we drop a perpendicular from the end of the direction vector on the x-axis, we get a right angled triangle

The magnitude of the side of the triangle on the x-axis denotes the east component of the ball

Using trigonometry, we find that the east component of the ball is:

125 * Cos(25 degrees)

125 * 0.9 = 112.5 i   (here, i denotes rightward direction on the x-axis)

North Component of the Ball:

this component is denoted by blue color in the image

Using trigonometry, we find that the North component of the ball is:

125* Sin(25 degrees)  (-j)      [j denotes upward movement on the y-axis, since the vector is acting downwards, we have used '-j']

125 * 0.42 (-j)

52.5 (-j) =   -52.5 j

Therefore the direction vector of the ball is 112.5 i - 52.5 j

where 112.5 i is the East Component and -52.5 is the North Component