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 roller coaster from problem #1 then tops a second hill at 15.0 m/s, how high is the second hill? 91.5 m 79.2 m 80.0 m 68.5 m

Consider an ordinary, helium-filled party balloon with a volume of 2.2 ft3. the lifting force on the balloon due to the outside air is the net resultant of the pressure distribution exerted on the exterior surface of the balloon. using this fact, we can derive archimedes’ principle, namely that the upward force on the balloon is equal to the weight of the air displaced by the balloon. assuming that the balloon is at sea level, where the air density is 0.002377 slug/ft3, calculate the maximum weight that can be lifted by the balloon. note: the molecular weight of air is 28.8 and that of helium is 4.

Gabby calls her cousin who lives in a different state and tells her to turn her radio to channel 98.7 so they can listen to their favorite song that is playing. her cousin turns her radio to 98.7, but does not hear the same song gabby hears. which most likely explains why?