Solving a Car's Travel in a Flat Circle - Can You Help?

[Xamfy19]

The question is :
A car travel in a flat circle of radius R. At a certain instant the velocity of the car is 18 m/s west and the total acceleration of the car is 2 m/s2 at 46 degrees north of west. What is R?

I simply used a = v2/R and obtained 162 m. I suspected the question should be more complicated than I thought. Can anyone help. Thanks.

 

[himanshu121]

The formula u applied is for a_n so u have to take the component which is in the direction of radius or it shoul be radial component of acceleration. and velocity should be the tangential velocity

 

[Xamfy19]

thanks, maybe more info needed

I took cos(46) of 2 m/s2 and used for the formula. It's not the correct answer. Do I need to figure out the linear speed? (apparently it is not 18 m/s)?
Thanks a lot.

 

[Doc Al]

Originally posted by Xamfy19
I took cos(46) of 2 m/s2 and used for the formula. It's not the correct answer. Do I need to figure out the linear speed? (apparently it is not 18 m/s)?

The linear speed is 18 m/s, nothing wrong with that.

Draw a picture of what's happening and you will see that you took the component of the acceleration incorrectly.

 

[Xamfy19]

should be sin instead of cos

I guess I've mistaken the direction 46 degrees north of west as west of north. I have just tried again and it worked. Thanks a lot.