Motion in Two and Three Dimensions

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The discussion focuses on a physics problem involving a rabbit sliding on ice with an initial velocity and constant acceleration. The correct unit vector notation for the rabbit's velocity after 3 seconds is derived as v = 6i + 4.2j, where "i" represents east and "j" represents north. The participants emphasize the importance of treating vector equations component-wise and including units in the final answers. There is a clarification that the problem asks for velocity and position, not just speed and distance. Overall, the conversation highlights the need for careful attention to vector notation in physics problems.
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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.
 
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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 traveled 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:
thegoosegirl42 said:

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.
 
Simon Bridge said:
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 traveled 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!
 
No worries.
A lot of physics is just treating the maths as a language.
 
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