Calculate the angle between the displacement vector and the force vector

[Absolutism]

Homework Statement

A force F = 8i-3i N acts on a particle that undergoes a displacement Δr = 2i + j m.
(b) What is the angle between F and Δr? (state your answer to three significant figures)

Homework Equations

Angle = cos-1 (A.B/ AB)

The Attempt at a Solution

W=13.1 J
AB= 8.5*2.23= 19
cos-1 (13.1/19)= 46.4

 

[BitterX]

I will assume that the force is $F=8\hat{i}-3\hat{j}$

the dot product between F and delta-r:
$(8,-3)\cdot (2,1) = 8\cdot 2 + (-3)\cdot 1 = 13$
the norm of F:
$||F||=\sqrt{8^2 +3^2}$
norm of delta-r :
$||\Delta r|| =\sqrt{1^2+2^2}$
I got 47.12 degrees but it seems you have used different conditions :/

 

[Absolutism]

I got 47.121 another time when I did not round, but even that gave me a wrong answer L: I am not sure what's wrong

 

[BitterX]

If you are sending it to some kind of online checking system:
a. Check to see if they want it in radians.
b. Check if all of the starting conditions are correct.
c. Take into consideration that they make mistakes too.

 

[asteriatic]

degrees

Based on the given information, the angle between the displacement vector (Δr) and the force vector (F) can be calculated using the formula: Angle = cos-1 (A.B/ AB). Plugging in the values, we get an angle of 46.4 degrees. This means that the displacement and force vectors are at an angle of 46.4 degrees with respect to each other.