Let the following polynomial represt the altitude in meters during the first 48

Question

Let the following polynomial represt the altitude in meters during the first 48 hours following the launch of a weather balloon:

h(t) = -0.12t^4 + 12t^3 - 380t^2 + 4100t + 220

Assume that the unit of t is hours.

(a) Use MATLAB together with the fact that the velocity is the first derivative of the altitude to determine the equation for the velocity of the balloon.

(b) Use MATLAB together with the fact that acceleration is the derivative of velocity, or the second derivative of the altitude, to determine the equation for the acceleration of the balloon.

(c) Use MATLAB to determine when the balloon hits the ground. Because h(t) is a fourth-order polynomial, there will be four answers. However, only one answer will be physically meaningful.

(d) Use MATLAB’s symbolic plotting capability to create plots of altitude, velocity, and acceleration from time 0 until the balloon hits the ground[which was determined in part (c)]. You’ll need three separate plots, since altitude, velocity and acceleration have different units.

(e) Determine the maximum height reached by the balloon. Use the fact that the velocity of the balloon is zero at the maximum height.

Explanation / Answer

int main(void)
{
/* Declare variables. */
int st,inc,et;
float alt,vel,max_alt=0,time,max_time;

/* Get user input from keyboard */
do
{
printf("Enter Start Time in Hrs. (0-48) :");
scanf("%d",&st);
}while(st<0 || st>48);

do
{
printf("Enter Increment in Time in Minutes (0-60) :");
scanf("%d",&inc);
}while(inc<0 || inc>60);

do
{
printf("Enter End Time in Hrs. (0-48) :");
scanf("%d",&et);
}while(et<0 || et>48);

/* To Display the Table */
printf(" Time Altitude Velocity ");
printf("--------------------------------------------- ");
for(long int i=(st*60);i<=et*60;i++)
{
time = (float)i/60;
alt = -0.13*pow(time,4)+12*pow(time,3)-380.0*pow(time,2)+4100*(time)+220;
vel = -0.48*pow(time,3)+36.0*pow(time,2)-760*(time)+4100;
/* to check for maximum altitude */
if(max_alt<alt)
{
max_alt = alt;
max_time = time;
}
/* to display the value for that interval*/
if(i%inc == 0)
{
printf("%f %f %f ",time,alt,vel);
}

}

printf("Maximum Altitude Reached : %f ",max_alt);
printf("Maximum Altitude Reached at time : %f hrs ",max_time);

/* Exit program. */
system("Pause");
return 0;
}

/*---------------------------------------------*/

Related Questions

Navigate

• Browse (All)
• Browse L
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.