# Car changing speed around a corner - find tangential and radial accel

## Homework Statement

A car changes speed as it turns from travelling due south to heading due east. When exaclty halfway around the curve, the cars velocity is 19m/s at 45° south of east. At this moment, the cars total acceleration is 3.0 m/s2 at 20° north of east.

Calculate the radial and tangential components of the cars acceleration, then calculate the radius of the turn

## Homework Equations

and tangential/centripetal acceleration is Δ|v|/Δt

## The Attempt at a Solution

I cant use either of these formulas to find either acceleration. Radius isnt given to find radial acceleration, and time isnt given to find tangential accel.

So from there I tried using the given total acceleration: 3.0m/s and 20° with
either the sine or cosine laws to find the acceleration components.

I ended up with some numbers that seemed unlikely (I need to figure out how to post formulas better..) so Im doubting that is how to solve the question.

What i do know is that once I find radial acceleration I can use that formula to find the Radius.

How about finding the angle between your acceleration vector given and the direction of the expected centripetal acceleration vector. Same, what is the angle between the expected tangential acceleration vector and the acceleration vector given?

How about finding the angle between your acceleration vector given and the direction of the expected centripetal acceleration vector. Same, what is the angle between the expected tangential acceleration vector and the acceleration vector given?

How would I find the angle of the expected radial accel vector with jsut the knowledge of the total accel vector being 20° north of east? Are the tangential accel and radial accel vectors perpendicular to each other? Therefore making it possible to use sin/cosine laws to find the missing angles/magnitudes?

If i use the sine law:

For tangential accel:

3m/s2/sin90° = b/sin70° so b would = 2.597m/s2

3m/s2/sin90° = c/sin20° so c = 3.064m/s2

But these numbers dont seem right..when i check the numbers my using

a2 = b + c2