Pennsylvania State University
International superspy Maria, flying at constant 208 km/h horizontally in a low-flying helicopter, wants to drop secret documents into her contact’ open car which is traveling at 156 km/h on level highway 78.0 g beneath. At what anglo (with the horizontal) should the car bc in her sights when the packet is released? Assume that helicopter and thc car arc traveling in the aforementioned management and that helicopter i8 over taking the car from behind.
Spymaster Chris, flying a constant 208 km/h horizontally in a depression-flying helicopter, wants to drop secret documents into her contact’south open auto which is traveling 156 km/h on a level highway 78.0 m below. At what angle (with the horizontal) should the car be in her sights when the packet is released (Fig. 3-55)?
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Okay, the speed of the helicopter is 208 kilometers per 60 minutes. Okay. And wants to driblet her documents into a car. So the speed of the car Is 156 kilometers per hr. That’southward pretty fast. Very fast. And the height is 78 meters. Well I’d similar to convert both of these dim meters per second. Then in that location’s 1000 meters in a kilometer And there’s 3600 seconds in an hour. So let me put these into the calculator. V equals 208 times 1000 divided by 3600. Gives me 58 and V sub C. I’m going to call that 5 sub two is 156 times A thou divided by 3600. That’s 42. Okay, the peak is this? And so the relative velocity is going to be the minus V. C. So I’m going to put that in. That’s going to be uh 16 meters per second. Okay now um if she’due south going to release a package, information technology’due south gonna fall like this. Um I’m going to apply the relative velocity and as well the time. Now the time to hit the footing uh is going to be determined by this. Why final is 0? Why initial is H. Y. Equals Y. Initial plus 5. Y. Initial T. Which is nothing minus i half G. T squared. So the time to striking the ground is going to be the square root Of two H over G. That’s supposed to be an H. two H over 1000. Okay, but the relative velocity. Um And I’m going to call this, can I phone call it D. D. Is Velocity, relative velocity times time, only fourth dimension is the square root of two H over Grand. And then I’d similar that horizontal distance to be that um to age Over G where H is 78. Okay. So D. Is going to exist 64 0.2 m. So Uh the distance is 64.ii yard. The nosotros demand to put D here on my calculator. The height Is 78 m. Okay. The question is at what angle in her sight? So I’m thinking that information technology’southward asking u.s.a. about this angle hither. Fate is going to be the inverse tangent of why? Which is H over acts which is D. And so the changed tangent of H. Over D. Mm. Yeah. 50 0.five degrees. Yes. Thank you for watching.
A Helicopter is Traveling at 860 Km/h
Originally posted 2022-08-05 14:59:32.