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

[Phys121VIU]

Homework Statement

A car changes speed as it turns from traveling due south to heading due east. When exactly 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

Radial acceleration is v²/R

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

The Attempt at a Solution

I can't use either of these formulas to find either acceleration. Radius isn't given to find radial acceleration, and time isn't 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 I am 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.

 

[r0wbrt]

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?

 

[Phys121VIU]

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 just 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

And for radial/centripetal accel:

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

But these numbers don't seem right..when i check the numbers my using

a² = ^b + c²

i come out with 4.01m/s² which doesn't = the given total accel...please help!

 

[rcgldr]

You're given both the direction of the velocity vector (45° south of east) and the acceleration vector (20° north of east). Use this information to determine the relative angle between velocity and acceleration.

 

[BlackStar]

tangential acceleration is in the direction of velocity, so the angle between tangential accel and total accel is 20+45=65 degrees.
centripetal acceleration is perpendicular to velocity and makes 45-20=25 degrees.
so you get 3sin65 and 3sin25 as answers
btw tangential and radial are by definition perpendicular directions.And also check your answer! c=3sin20$\neq$3.024