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You are in a hot-air balloon that, relative to the ground, has a velocity of 6.0 m/s in a direction due east. You see a hawk moving directly away from the balloon in a direction due north. The speed of the hawkrelative to you is 2.0 m/s. What are the magnitude and direction of the hawk’s velocity relative to the ground? Express the directional angle relative to due east.

$v_{H G}=6.325 \mathrm{m} \cdot \mathrm{s}^{-1}$$\theta=18.43^{\circ}$

Physics 101 Mechanics

Chapter 3

Kinematics in Two Dimensions

Motion in 2d or 3d

University of Michigan - Ann Arbor

Hope College

University of Winnipeg

McMaster University

Lectures

04:01

2D kinematics is the study of the movement of an object in two dimensions, usually in a Cartesian coordinate system. The study of the movement of an object in only one dimension is called 1D kinematics. The study of the movement of an object in three dimensions is called 3D kinematics.

10:12

A vector is a mathematical entity that has a magnitude (or length) and direction. The vector is represented by a line segment with a definite beginning, direction, and magnitude. Vectors are added by adding their respective components, and multiplied by a scalar (or a number) to scale the vector.

02:22

You are in a hot-air ballo…

03:41

02:43

you are in a hot-air ballo…

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3) You are in a hot-air ba…

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A weather station releases…

01:45

An airplane has a velocity…

00:35

If the net force on a hot-…

02:25

A small airplane is flying…

05:24

A small plane is flying di…

The speed of an object and…

06:56

The nose of an ultralight …

05:51

Ground Speed and Direction…

02:53

An airplane flies due nort…

16:33

So the question states that a hot air balloon moves due east at six meters per second relative to the ground. So we'll call the origin here the ground and it's not moving at all. And the hot air balloon is moving to the right or do eased at six meters per second. And we're also told that the person in the hot air balloon sees a hawk moving north straight due north at two meters per second. And our task is to find what the magnitude of the velocity is of the hawk relative to the ground, which is at the origin. So basically, we're trying to find what this vector here is. So to do this, it's actually pretty simple. We no that to find the magnitude of a victor. So, for example, Viktor B. It's just the square root of the horizontal component squared, plus the vertical component squared, and in this case they're both given to us. So the horizontal component is six meters per second and the vertical component is two meters per second. So when we plug this in, we get the square root of 36 plus for which is equal to square root of 40 which is the same thing as six point 3 to 5 meters per second. So this the magnitude of the Wasim of the Hawk relative to the ground. Now we're also asked to find what this angle is, which is the, uh, angled given by, um, the vector capital V from due east. So to find this, we can just take the tannin vers which is going to be opposite over Jason, where in this case, it's two meters per second over six meters per second and this will give us our angle data that we want to find and when we calculate this, we end up getting 18.43 degrees.

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