Kinematics and Dynamics

6.) An airplane flies due south with respect to the ground at an air speed of 900 km/h for 2.0 hr before turning and moving southwest with respect to the ground for 3.0 hr. During the entire trip, a wind blows in the easterly direction at 120 km/h. (a) What is the plane's average speed with respect to the ground? (b) What is the plane's average velocity with respect to the ground? (c) What is the final position vector?

7.) Five forces, all of the same magnitude F, act on an object of mass m at the origin of the coordinate system. Two of the forces are aligned along the x-axis; one is oriented in the +x direction and one in the -x direction. Two other forces are similarly aligned with the z-axis. The fifth force points int he +y direction. What are the direction and magnitude of the acceleraation of the object? If we had specified the forces in a different order, would the answer have been different?

8.) A father pulls his identical twins on identical sleds tied one after the other. He exerts a force F that makes an angle of 30 degrees with the horizontal and that leads to an acceleration of the two sleds. What is the tension in the rope that he is pulling? What is the tension in the rope that connects the front sled to the rear sled? The mass of each sled plus its twin is m. Assume that there is no friction between the sleds runners and the snow surface.

9.) A force of magnitude 8.0 N pushes on a horizontally stacked set of blocks on a frictionless surface with masses m1 = 2.0 kg, m2 = 3.0 kg, m3 = 4.0 kg. (a) What is the acceleration of the stack? (b) What are the forces on block 1 as well as the net force on this block? (c) Repeat part b for block 2. (d) Repeat part b for block 3.