# Question:Optimization hw 02 help

## Question:Optimization hw 02 help

question 2 of my homework is actually abit more simple imo. i think i performed all the operations correctly but however my 3dplot shows just a flat plane. i dont think thats right. if someone could take a look at my code in reference to this question. it would be great.

Suppose that a baseball is hit from 5 feet off of the ground with an initial velocity of 40 feet per second at an angle of above the horizontal. Let the horizontal and vertical components of the position, velocity, and acceleration be denoted respectively by and . Assume that the only acceleration is due to gravity (i.e, ).

a) If , plot the parametric equations over the time period that the ball is in the air.

b) Clear in maple by typing theta:='theta'; Now, suppose that we write in Cartesian form by solving for t: t:=solve(rx=x,t); Typing in ry should now yield a function that involves only x and . Make a 3-dimensional plot of for ,

ax:=0;ay:=-32;
0
-32
vx:=int(ax,t)+C1;
C1
vy:=int(ax,t)+C2;
C2
v0:=40;
40
theta:=Pi/3;
1
- Pi
3
C1:=solve(subs(t=0,vx)=v0*cos(theta),C1);
20
C2:=solve(subs(t=0,vy)=v0*sin(theta),C2);
(1/2)
20 3
vx; vy;
20
(1/2)
20 3
rx:=int(vx,t)+C3;
20 t
ry:=int(vy,t)+C4;
(1/2)
20 3 t + 5
C3:=solve(subs(t=0,rx)=0,C3);
0
C4:=solve(subs(t=0,ry)=5,C4);
5

ry;
(1/2)
20 3 t + 5
plot([rx, ry, t = 0 .. infinity]);

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