When the velocity v of an object is very large, the magnitude of the force due to air resistance is proportional to v squaredv2 with the force acting in opposition to the motion of the object. A shell of mass 33 kg is shot upward from the ground with an initial velocity of 800800 m/sec. If the magnitude of the force due to air resistance is (0.10.1)v squaredv2, when will the shell reach its maximum height above the ground? What is the maximum height? Assume the acceleration due to gravity to be 9.81 m divided by s squared9.81 m/s2.

Aspring has a relaxed length of 33 cm (0.33 m) and its spring stiffness is 6 n/m. you glue a 76 gram block (0.076 kg) to the top of the spring, and push the block down, compressing the spring so its total length is 15 cm. you make sure the block is at rest, then at time t=0 you quickly move your hand away. the block begins to move upward, because the upward force on the block by the spring is greater than the downward force on the block by the earth. calculate y vs. time for the block during a 0.09-second interval after you release the block, by applying the momentum principle in three steps each of 0.03-second duration.