i found magnitude how do you find direction

Question

A train slows down as it rounds a sharp horizontal turn, slowing from 83.2 km/h to 58.9 km/h in the 13.4 s that it takes to round the bend. The radius of the curve is 143 m. Compute the acceleration at the moment the train speed reaches 58.9 km/h. Assume that it continues to slow down at this time at the same rate

Magnitude
1.94

Correct: Your answer is correct.
m/s2
Direction


Incorrect: Your answer is incorrect.

Answer 1

Hi Porcia!

 

When calculating the direction, you can look at the radial and tangential directions as perpendicular components of the overall acceleration (this is probably how you calculated the magnitude).  They specify a resultant at some angle with respect to each component.  Unless the question specifies where you are to measure this angle from, you get to choose.

 

Let's choose the angle with respect to the tangential velocity.  In that case, the radial component is the "opposite" side, and the tangential is the "adjacent" side.  Therefore, you can get the angular direction θ of the resultant with respect to the tangential component by using:

 

tan(θ) = a_r/a_t = (1.87 m/s²)/(0.5 m/s²) = 3.74

θ = tan^-1(3.74)

 

If you are required to give the angle with respect to the radial direction, you just switch which component is opposite and which is adjacent.

 

I hope this helps!  If you have any further questions, just let me know.