Motion in Two and Three Dimensions

  • #1

Homework Statement


A frightened rabbit runs onto a large area of level ice that offers no resistance to sliding, with an initial velocity of 6m/s toward the east. As the rabbit slides across the ice, the force of the wind cases it to have a constant acceleration of 1.4 m/s^2, directed due north. In unit vector notation, what are the rabbit's (a) velocity and (b) position when it has slid for 3s?

Homework Equations


Vf=Vo+at
x=xo+Vo*t+.5*a*t

The Attempt at a Solution


I got the total answers of unit vector added up which for a is 10.2 and for b 24.3 but I don't know how you are to solve it in unit-vector notation.
 

Answers and Replies

  • #2
Simon Bridge
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if n is a unit vector pointing north and e is a unit vector pointing east... use those to write an equation describing the velocity as follows...

"The velocity of the rabbit is so-fast north and so-fast east"

the first part is v= for "the velocity of the rabbit is"
the word "and" turns into a plus sign
the directions are replaced by their unit vectors.

Take care though... you must include units with your answer; your answers do not answer the questions... you have calculated the speed and distance travelled and you are asked for the velocity and position (they should have said displacement), you also have the wrong number for speed. Revise your notes on vectors.
 
Last edited:
  • #3
HallsofIvy
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Homework Statement


A frightened rabbit runs onto a large area of level ice that offers no resistance to sliding, with an initial velocity of 6m/s toward the east. As the rabbit slides across the ice, the force of the wind cases it to have a constant acceleration of 1.4 m/s^2, directed due north. In unit vector notation, what are the rabbit's (a) velocity and (b) position when it has slid for 3s?

Homework Equations


Vf=Vo+at
x=xo+Vo*t+.5*a*t

The Attempt at a Solution


I got the total answers of unit vector added up which for a is 10.2 and for b 24.3 but I don't know how you are to solve it in unit-vector notation.
Taking "i" as the unit east vector and "j" as the unit north vectors (equivalent to Simon Bridge's "e" and "n"), then, the initial velocity vector, "6m/s toward the east" is 6i and the constant acceleration vector, "1.4 m/s^2, directed due north" is 1.4j.
v= v0+ at= 6i+ 1.4j(3)= 6i+ 4.2j.

Your equations "Vf= Vo+ at" and "x= xo+ Vot+ .5at", since they involve vectors, must be done "component wise". That is, if u= ai+ bj and v= ci+ dj, u+ v= (a+ c)i+ (b+ d)j.
 
  • #4
if n is a unit vector pointing north and e is a unit vector pointing east... use those to write an equation describing the velocity as follows...

"The velocity of the rabbit is so-fast north and so-fast east"

the first part is v= for "the velocity of the rabbit is"
the word "and" turns into a plus sign
the directions are replaced by their unit vectors.

Take care though... you must include units with your answer; your answers do not answer the questions... you have calculated the speed and distance travelled and you are asked for the velocity and position (they should have said displacement), you also have the wrong number for speed. Revise your notes on vectors.
Thank you I was just overthinking something simple!
 
  • #5
Simon Bridge
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No worries.
A lot of physics is just treating the maths as a language.
 

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