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

John throws .4 kg ball with velocity of 18 m/s. hits .2 kg bottle and bottle flies 25 m/s. how fast is ball traveling after hitting the bottle?

Oxygen and nutrients are moved through the body by the: a. circulatory system c. lymphatic system b. digestive system d. reproductive system

1. the materials manager for a billiard ball maker must periodically place orders for resin, one of the raw materials used in producing billiard balls. she knows that manufacturing uses resin at a rate of 50 kilograms each day, and that it costs $.04 per day to carry a kilogram of resin in inventory. she also knows that the order costs for resin are $100 per order, and that the lead time for delivery is four (4) days.2. at what point should resin be reordered? a. 0 kilograms remainingb. 50 kilograms remainingc. 200 kilograms remainingd. 400 kilograms remaininge. 500 kilograms remaining3. if order size was 1,000 kilograms of resin, what would be the length of an order cycle? a. 0.05 daysb. 4 daysc. 16 daysd. 20 dayse. 50 days4. if the order size was 1,000 kilograms of resin, what would be the average inventory level? a. 50 kilogramsb. 200 kilogramsc. 500 kilogramsd. 800 kilogramse. 1,000 kilograms5. if the order size was 1,000 kilograms of resin, what would be the daily total inventory costs, excluding the cost of the resin? a. $5b. $10c. $20d. $25e. $40