The coordinates of a bird flying in the xy-plane are given by x(t...

Question

The coordinates of a bird flying in the xy-plane are given by x(t) = αt and y(t) = 3.0 m − βt2, where α = 2.4 m/s and β = 1.2 m/s2. (a) Sketch the path of the bird between t = 0 and t = 2.0 s.

Accepted Answer

Hi, everybody. Let's get started. So in the jungle, the position of the monkey in the Y Z plane is given by the coordinates Y of T equals A T minus 0.4 m and Z of T equals B T squared meters. And then we're actually given A and B A is equal to 1.1 m per second and B is equal to 0.95 m per second squared. So we have A is a velocity and B is an acceleration. And then we need to sketch the path that the monkey takes for 10 seconds from its initial position. So we have here a linear equation for, for why. And then an exponential equation for the easy access and recalling what those, what those are for, we can break them up into their components to determine how this graph is gonna look. So first looking at our linear equation here, we can see that it of course follows the format of Y equals MX plus B. And knowing that B is our y intercept, we can go over here and see that our corresponding B is a negative 0.4. So we know that in the Y axis on the bottom, in these images, we should have a Y intercept of negative 0.4. So if we look at our graph choices here, we can already eliminate some of these answers. B is incorrect because it does not have, it is an intercept in the positive range up here. So that's not going to be right. D is also wrong for the same reason why intercept is zero here. And that doesn't line up with what we've calculated. So that leaves us with a and see how can we tell them apart. So we will go to our next equation here are exponential. And If we do a little math here, so we want to figure out the sketch, we want to sketch the path that the monkey takes for 10 seconds from its initial position. So since we have A T in our equations, we can actually take our exponential and plug in time in order to and uh and of course, we're given B and we can calculate that to determine where the monkey should be at the end of its path. So if we take B 0.95 m per second squared, it's accelerating multiply that by T squared, which in this case is going to be 10, that's our time, That's going to give us 95 m/s square. So if we look at our graphs again, we should be looking for a final, a final Z axis value of 95 m per second squared. So if we compare A and C here, we can see, see has, See all the way up here, stops it 1 10, that's a little bit too high. So if we, so we can look at a and see that A does in fact have the correct Why intercept and it also appears to stop at about 95, which is what we calculated. So that means a must be the correct answer. Thank you.

The coordinates of a bird flying in the xy-plane are given by x(t) = αt and y(t) = 3.0 m − βt2, where α = 2.4 m/s and β = 1.2 m/s2. (a) Sketch the path of the bird between t = 0 and t = 2.0 s.

Watch next