F~ and ∆~r are vectors. F~ = Fx ˆı + Fy ˆ + Fz kˆ where Fx = 28.3 N, Fy = 62.7 N, Fz = −71.2 N, and ∆~r = ∆x ˆı + ∆y ˆ + ∆z kˆ, where ∆x = 44.8 m, ∆y = -11.6 m, ∆z = −10.1 m. (a) What is the magnitude of F~ (N)? (b) What is the magnitude of ∆~r (m)? (c) What is the scalar product of F~ and ∆~r (J)? (d) What is the angle between F~ and ∆~r (degrees)? (e) How much work would be done if this force acted on a 30 kg space ship while it experienced a displacement of ∆~r (J)?

The force will determine the acceleration.

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

Astudent pushes a 60-n block across the floor for a distance of 10 m. how much work was done to move the block