Peregrine falcons are known for their maneuvering ability. In a tight circular turn, a falcon can attain a centripetal acceleration 1.5 times the free-fall acceleration. What is the radius of the turn if the falcon is flying at 25 m/s?

Video transcript

Everyone in this problem, we're told that a plane flies in a completely horizontal circle at a constant speed of 300 kilometers per hour. And we're asked to calculate the diameter of the circle. If the plane's radio acceleration is equal to twice the gravitational acceleration, we're given four answer choices all in meters. Option A 41 option B 708 option C 1634 and option D 8155. All right. So we want to find the diameter, we're giving the speed, we're told some information about the radial acceleration. So let's recall the following equation. We can write that the radial acceleration A R is equal to the speed V squared divided by the radius R right now. This equation does not have the diameter in it, but the radius and the diameter are related. I recall that the radius is going to be half of the diameter. So let's rearrange this equation for R that's gonna allow us to solve or the diameter D. OK. So we can write that the radius R is going to be equal to the speed V squared. Divided by the radial acceleration A R like we just mentioned, the radius R is going to be equal to the diameter D divided by two. And the diameter D is what we are looking for. And that's gonna be equal to V squared divided by A R. OK. So now we have this equation with the diameter in it that we are interested in, we can multiply both sides by two. So we get D is equal to two V squared divided by A R. Yeah, what can we do about this? OK. We're given this speed, we want it in our standard units. OK. So the speed V that we're given is 300 kilometers per hour. We wanna convert this into meters per second. So we're gonna multiply and first we're gonna multiply by 1000 m per kilometer. And we know there are 1000 m in every kilometer and then the unit of kilometer will divide out. So we're gonna multiply by one hour provided by 3600 seconds because we know that there are 3600 seconds in every hour, the unit of our world divide out. And so we're left with meters per 2nd and 300 multiplied by 1000 divided by 3600. And we get about 83.33 repeated meters per second. OK? So that's gonna be that speed V in our equation. Now, the radial acceleration A R we're told that that is going to be two twice the gravitational acceleration. And so that's gonna be two multiplied by the acceleration due to gravity G. And that's gonna be two multiplied by 9.81 m per second squared. We're just gonna leave it like that for now. OK. So that's our radial acceleration. Now, we have everything we need to calculate this diameter of the circle. So substituting in these values, we get that the diameter D is gonna be two multiplied by 83.33 repeated meters per second, all squared divided by two multiplied by 9.81 m per second squared. When we work all of this out, we get to the diameter of the circle. It is about 707.89 m comparing this to our answer choices and our answer choices are rounded to the nearest meter. If we round to the nearest meter, our answer is going to be 708 m which corresponds with answer choice B that's it for this one. Thanks everyone for watching. See you in the next video.