hi, could You help me to write script(program) with maple( maple 13) exercise....?
1) The velocity of a freely falling object near Earth's surface is described by the equation
where v is the velocity, g=9.8m/s^2 . Write a program that employs the Euler method to compute to solution to (1.1); that is, calculate v as a function of t. For simpilicity, assume that the initial velocity is zero-that is, the object starts from rest-and calculate the solution for times t=0 to t=10 s. Repeat the calculation for several different values of the time step, and compare the results with the exact solution to (1.1). It turns out that for this case the Euler mathod gives the exact results. Verify this with your numerical results and prove it analytically.
2)The position of an object moving horizontally with a constant velocity, v, is described by the equation
Assuming that the velocity as a constatn, say v-=40 m/s, use the Euler method to solve (1.2) for x as a function of time. Compare your result with the exact solution.
3) It is often the case that the frictional force on an object will increase as the object moves faster. A fortunate example of this is a parachutist; the role of the parachute is to produce a fractional force due to air drag, which is larger that would normally be the case without the parachute. The physics of air drag will be discussedd in more detail in the next chapter. Here we cobsider a very simple wxaple in which the fractional force depends on the velocity. Assume that the velocity of an object obeys an equatiuon of the form
where a and b are costans. You could think of a as coming an applied force, such as gravity, while b aries from friction. Note that the frictional force is negative (we assume b>0), so that is opposes the motion, and that it increses in magnitude as the velocity increases. Use Euler method to silve (1.3) for v as function of time . A convenient choise of parameters is a= 10 , b=1. You should that v approaches a constant value at long times; this is called the terminal velocity.
soeey for my bad Engish.