A 6.00-kg crate is suspended from the end of a short vertical rope of negligible mass. An upward force F(t) is applied to the end of the rope, and the height of the crate above its initial position is given by y(t)=(2.80m/s)t+(0.610m/s^3)t^3. What is the magnitude of F when t = 4.00 s?

An important dimensionless parameter concerned with very high-speed flow is the mach number, defined as v/c, where v is the speed of the object such as an airplane or projectile, and c is the speed of sound in the fluid surrounding the object. for a projectile traveling at 1170 mph through air at 50 ˚f and standard atmospheric pressure, what is the value of the mach number?