Chapter 5.3, Problem 25E

The kinetic energy E of an object varies jointly with the object’s mass m and the square of the object’s velocity v . An object with a mass of 50 kilograms traveling at 16 meters per second has a kinetic energy of 6400 joules. What is the kinetic energy of an object with a mass of 70 kilograms traveling at 20 meters per second?

Transient Orifice Flow: Water is discharged from a reservoir through a long pipe as shown. By neglecting the change in the level of the reservoir, the transient velocity of the water flowing from the pipe, vt), can be expressed as: - Reservoir v(t) V2gh = tanh V2gh) Pipe Where h is the height of the fluid in the 7- reservoir, L is the length of the pipe, g is the acceleration due to gravity, and t is the time elapsed from the beginning of the flow Transient Orifice Flow: Determine the helght of the fluid in the reservoir at time, t= 2.5 seconds, given that the velocity at the outfall, vt) = 3 m/s, the acceleration due to gravity, g = 9.81 m/s? and the length of the pipe to outfall, L= 1.5 meters. Reservoir v(t) V2gh = tanh 2L 2gh water Pipe Hint: Transform the equation to a function of form: fih) = 0 Solve MANUALLY using BISECTION AND REGULA-FALSI METHODS, starting at xn = 0.1, Kg =1, E = 0.001 and If(*new)l < E

A4) The position of a hummingbird flying along a straight line in t seconds is given by S(t) = 2t - 20t meters. [ 1 mark ] (a) Determine the velocity of the bird at t = 3 sec. [0.25 mark] (b) Determine the acceleration of the bird at t = 3 sec. [0.25 mark] (c) Determine the acceleration of the bird when the velocity equals 0. [0.5 mark]