A plane flying at 78.2 m/s [W32°S] takes 42 seconds to change its velocity to 78.2 m/s [S32°E]. a) Solve for the change in velocity of the plane algebraically, resolving vectors into their x- and y-components. b) What was the average acceleration of the plane over this time interval? c) Explain why the speed of the plane didn't change and yet the plane underwent acceleration. Please label sketches with events as well as GRASS and explanations to show your work. Please label triangle sides. Remember to have the magnitude rounded to a reasonable number of sig figs, the unit and the direction (if needed) in your answers.

A plane flying at 78.2 m/s [W32°S] takes 42 seconds to change its velocity to 78.2 m/s [S32°E]. a) Solve for the change in velocity of the plane algebraically, resolving vectors into their x- and y-components. b) What was the average acceleration of the plane over this time interval? c) Explain why the speed of the plane didn't change and yet the plane underwent acceleration. Please label sketches with events as well as GRASS and explanations to show your work. Please label triangle sides. Remember to have the magnitude rounded to a reasonable number of sig figs, the unit and the direction (if needed) in your answers.