Calculating Time for a 90 Degree Turn in Circular Motion

AI Thread Summary
To calculate the time for a pilot to make a 90-degree turn with a radius of 50.0 meters at a speed of 26.0 m/s, the formula used is time = 1/4 * 2πR/v. This formula derives from the total time to complete a full circle, T = 2πR/v, divided by four, since a 90-degree turn is one-fourth of a full circle. The discussion clarifies that the tangential acceleration equation is unnecessary for this calculation. The key takeaway is that using the constant speed and the radius allows for straightforward computation of the time required for the turn. Understanding these relationships is essential for solving similar problems in circular motion.
billu77
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Homework Statement



A pilot makes a turn of radius 50.0 meters at a speed of 26.0m/sec. How long will it take him to make a 90 degree turn?

Homework Equations



tangential acceleration = final velocity - initial velocity/time

The Attempt at a Solution



tangential acceleration = final velocity - 26/t
stuck at this point...unable to find final velocity from here?
 
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You actually don't need that equation. How much distance does he have to cover to turn 90 degrees? How fast is he turning? (Hint: it's 26.0 m/s.) How much time does it take?
 
Since speed is constant, time = 1/4* 2πR/v.
 
rl.bhat said:
Since speed is constant, time = 1/4* 2πR/v.

thanks...could u please explain how u got to that formula.
the one I have in book is:

T= 2\pir/v

thanks
 
That T= 2LaTeX Code: \\pi r/v is the time it needs to cover a full circle (360*)
So what's the time to cover 1/4 360*?

Thats time=T/4 = 1/4* 2πR/v.
 

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