Hockey puck b rests on a smooth ice surface and is struck by a second puck a, which has the same mass. puck a is initially traveling at 16.0 m/s and is deflected 21.0 ∘ from its initial direction. assume that the collision is perfectly elastic.
a) find the final speed of the puck bafter the collision.
b) find the final speed of the puck aafter the collision.
c) find the direction of b's velocity after the collision.

This is important 1. what happens to the speed of molecules in water vapor when it condenses to form a liquid? (2 points) the molecules slow down. the molecules speed up. the molecules slow down and then speed up. the molecules speed up and then slow down. 2. how might human activities change to compensate for a decrease in water supplies? (2 points) humans might build a factory. humans might build drainage systems. humans might extract more water from the ground. human behavior does not change because of the water cycle. i'll be grateful if anyone can answer these 2 questions !

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

Aleaky 10-kg bucket is lifted from the ground to a height of 15 m at a constant speed with a rope that weighs 0.7 kg/m. initially the bucket contains 45 kg of water, but the water leaks at a constant rate and finishes draining just as the bucket reaches the 15-m level. find the work done. (use 9.8 m/s2 for g.) show how to approximate the required work by a riemann sum. (let x be the height in meters above the ground. enter xi* as xi.) lim n → ∞ n (9.8)(45−3 xi) i = 1 δx express the work as an integral. 0 dx evaluate the integral. (round your answer to the nearest integer.) j