Aball of mass m is tossed vertically upward from the ground with initial velocity v. air resistance must be taken into account and its force is proportional to the square of the veloc- ity. in addition, assume the gravitational force is constant. let h(t) be the height above the ground then newton's second law leads to the initial value problem (a) find the dimensions of the constant a. (b) use dimensional analysis to find a formula for the height h of the ball in terms of t and all the parameters in the problem. identify all the dimensionless quantities. (c) introduce a useful set of dimensionless variables and parameters into the initial value problem so that there is only one parameter left multiplying the air resistance term. you need to define dimensionless time r and height y - the class notes might be useful. (d) solve the new dimensionless initial value problem exactly and compare with the prob- lem without air resistance