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

In summary, the problem involves a supersonic plane with a speed of 2340 km/hr taking a 45 degree turn in a horizontal circle at a banking angle of 65 degrees. To find the time required to complete the turn, the centripetal force formula and a free body diagram must be used to calculate the radius of the turn. This problem is similar to the "moving car on a frictionless, banked road" problem and requires knowledge of circular motion and kinematics.
  • #1
laxbear99
1
0

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
 
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  • #2
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.
 

1. What is circular motion?

Circular motion is the movement of an object along a circular path. This means that the object is constantly changing direction while maintaining the same distance from a fixed point, known as the center of the circle.

2. What causes circular motion?

Circular motion is caused by a force acting on an object, known as the centripetal force. This force pulls the object towards the center of the circle and keeps it moving along the circular path.

3. How is circular motion different from linear motion?

The main difference between circular motion and linear motion is the path that the object follows. In circular motion, the object moves along a circular path, while in linear motion, the object moves along a straight path.

4. How do you calculate the speed of an object in circular motion?

The speed of an object in circular motion can be calculated by dividing the distance traveled by the time it takes to travel that distance. This is also known as the average speed. However, in circular motion, the speed is constantly changing, so the instantaneous speed at any given point is calculated using the derivative of the distance with respect to time.

5. What are some real-life examples of circular motion?

Some examples of circular motion in everyday life include the rotation of the Earth around the Sun, the motion of a car around a roundabout, and the spinning of a merry-go-round. Other examples include the motion of a satellite in orbit and the swinging of a pendulum.

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