- #1
tifa8
- 14
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Hi ! I have a intemediate calculus problem. I am seeing right now all about curves and motion curves.
Show that 1. the path of a particle lies on a sphere if its displacement and velocity are always perpendicular
2.show that if the particle moves with constant speed then the velocity and acceleration are penperdicular.
1.I think that it is obvious that it lies on a sphere. however I really don't know how to demonstrate that...
if i consider the displacement as r(t)=xi+yj+zk
then r(t).v(t)=0
=>r(t).r'(t)=0
=>xx'+yy'+zz'=0
but it is totally different from a sphere equation which is x^2+y^2+z^2=R^2
2. I don't know if my reasoning is true
since v is constant then v' is equal to zero, thus a is equal to zero
so a.v=0.v=0 so a and v are perpendicular. However, a is a zero vector which I think is quite strange...
thank you for your help
Homework Statement
Show that 1. the path of a particle lies on a sphere if its displacement and velocity are always perpendicular
2.show that if the particle moves with constant speed then the velocity and acceleration are penperdicular.
Homework Equations
The Attempt at a Solution
1.I think that it is obvious that it lies on a sphere. however I really don't know how to demonstrate that...
if i consider the displacement as r(t)=xi+yj+zk
then r(t).v(t)=0
=>r(t).r'(t)=0
=>xx'+yy'+zz'=0
but it is totally different from a sphere equation which is x^2+y^2+z^2=R^2
2. I don't know if my reasoning is true
since v is constant then v' is equal to zero, thus a is equal to zero
so a.v=0.v=0 so a and v are perpendicular. However, a is a zero vector which I think is quite strange...
thank you for your help