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Problem 58 Hard Difficulty

Spiraling up. It is common to see birds of prey rising upward on thermals. The paths they take may be spiral-like. You can model the spiral motion as uniform circular motion combined with a constant upward velocity. Assume a bird completes a circle of radius 8.00 $\mathrm{m}$ every 5.00 $\mathrm{s}$ and rises vertically at a rate of 3.00 $\mathrm{m} / \mathrm{s} .$ Determine: (a) the speed of the birc relative to the ground; (b) the bird's acceleration (magnitude) and direction); and (c) the angle between the bird's velocity vector and the horizontal.

Answer

a) 8.11 $\mathrm{m} / \mathrm{s}$
b) 9.48 $\mathrm{m} / \mathrm{s}^{2}$
c) $\left[21.7^{\circ}\right]$

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Physics 101 Mechanics

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Video Transcript

So we have a bird with centripetal with uniform circular motion. However, it is also moving in the positive. Why direction? So we have a radius of eight cent rather eight meters, so it's flying around in a circle with a radius of eight meters and it makes one revolution every five seconds. So as a period essentially of five seconds, it also has a V y of three ministers. Second, because that is as it is, moving in a certain as the birds moving in a circle. It is also moving up so we can save these of acts simply equals the circumference of this 18 year, 88 meter radius circle divided by the period. So this would be two pi r divided by t and this would be to pi times eight, divided by five and this is giving us 10.5 meters per second now to find the magnitude of the velocity vector, we can say that the magnitude is going to be three squared plus 10.5 squared all 2 1/2 power and this is giving us 10 point for nine meters per second. So this would be the velocity vector The linear velocity vector of the bird. Now for part B is asking us for the radio acceleration or so we can say that a and the wind direction is going to be zero me after second. Because thie why thie velocity and the Y direction is going to be constant. And we can say that the radio exploration was in triple exploration. In this case would be the X squared divided by our and this would be 10.5 squared, divided by eight. And this is giving us 12.63 meters per second squared now. It wants us to find the angle of the linear velocity with respect to the horizontal. So for part, see, we simply say that Fada Ah, it's going to be ableto are 10 of the wine component so three divided by the ex component 10.5 so this would be equal to 16.6 degrees. And then again, this is for this is going to be above the horizontal direction of the velocity factor with respect to the horizontal. And that is the end of the solution. Thank you for watching

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