The earth rotates once per day about an axis passing through the north and south poles, an axis that is perpendicular to the plane of the equator. Assuming the earth is a sphere with a radius of 6.38 x 106 m, determine the speed and centripetal acceleration of a person situated (a) at the equator and (b) at a latitude of 12.0 ° north of the equator.

A carnival merry-go-round rotates about a vertical axis at a constant rate. A man standing on the edge has a constant speed of 3.30 m/s and a centripetal acceleration of magnitude 2.01 m/s². Position vector locates him relative to the rotation axis. (a) What is the magnitude of 7? What is the direction of 7 when a is directed (b) due east and (c) due south? (a) Number (b) (c) Units

A pilot flies with a plane 20 km northward with an angle of 60 east ➚ , then 30 km to the east ⮕ , then 10 to the  north ⬆ , what is its distance from the start and what is its direction

At a football game, imagine the line of scrimmage is the y-axis. A player, starting at the y-axis, runs 8.50 yards, back (in the −x-direction), then 15.0 yards parallel to the y-axis (in the −y-direction). He then throws the football straight downfield 55.0 yards in a direction perpendicular to the y-axis (in the +x-direction). What is the magnitude of the displacement (in yards) of the ball?  yards (b) What if? The receiver that catches the football travels 64.0 additional yards at an angle of 45.0° counterclockwise from the +x-axis away from the quarterback's position and scores a touchdown. What is the magnitude of the football's total displacement (in yards) from where the quarterback took the ball to the end of the receiver's run?