How Long Does It Take a Supersonic Plane to Complete a 45-Degree Turn?

[laxbear99]

Homework Statement

A supersonic plane with a speed of 2340 km/hr takes a 45 degree turn flying in a horizontal circle at a banking angle of 65 degrees. What is the time required to complete a turn under these conditions?

The Attempt at a Solution

my teacher hasnt even tought us how to do stuff like this but i think it involves circular motion and kinematics? I'm lost

 

[collinsmark]

Hello laxbear99,

Welcome to Physics Forums!

Next time, please use the provided template, and list any equations which might/should be relevant to the problem statement.

This supersonic plane problem is essentially just another version of the "moving car on a frictionless, banked road problem." It involves centripetal force, so you'll need your centripetal force formula for part of this.

Draw a free body diagram (FBD). It might help to draw the diagram as seen from the rear of the banked plane, such that "up" points toward the top of the page, "down" points toward the bottom of the page, and the plane is accelerating (due to the turning) to the right side of the page. Use the FBD, the centripetal force formula, and the information in the problem statement to calculate the radius of the turn.

I'll let you take it from there.