3) A spacecraft on its way to Mars has small rocket engines mounted on its hull; one on its left surface and one on its back surface. At a certain time, both engines turn on. The one on the left gives the spacecraft an acceleration component in thex direction ofa_x = 5.10 m/s², while the one on the back gives an acceleration component in they direction ofa_y = 7.30 m/s². The engines turn off after firing for640 s, at which point the spacecraft has velocity components ofv_x =3665 m/s andv_y =4116 m/s. What was the magnitude and the direction of the spacecraft's initial velocity before the engines were turned on? Express the magnitude as m/s and the direction as an angle measured counterclockwise from the +x axis.

magnitude= m/s

direction= counterclockwise from the +x-axis

5) You are walking around your neighborhood and you see a child on top of a roof of a building kick a soccer ball. The soccer ball is kicked at45 from the edge of the building with an initial velocity of13 m/s and lands71 meters away from the wall. How tall, in meters, is the building that the child is standing on?

7) A spaceship is traveling through deep space towards a space station and needs to make a course correction to go around a nebula. The captain orders the ship to travel1.1 10⁶ kilometers before turning 70 and traveling2.7 10⁶ kilometers before assuming the path towards the space station. If the captain had not ordered a course correction, what would have been the magnitude (in kilometers) and direction (in degrees counterclockwise from the +x-axis) of the path of the spaceship if it had traveled through the nebula?

magnitude= 3.2451e6 km

What is the angle of direction?

8) Two position vectors lie in a plane. The first, vectorr_A, points at an angle of 20 below the positivex-axis and has a magnitude of59.5 m. The second, vectorr_B, points at an angle of55.0 above the positivex-axis and has a magnitude of 75 m.

1. What would this diagram look like?
2. What is the magnitude, in meters, and what is the direction of vectorr_C, in degrees? Give the direction as an angle measured counterclockwise from the positivex-axis.

magnitude=

direction= (counterclockwise from the +x-axis)