Quiz 3: Motion in Two Dimensions

Physics & Astronomy

Solution: Neither the x component of the vector nor the y component of the vector can be greater than the magnitude of the vector. Because, we calculate the magnitude of the vector by using the Pythagoras theorem, that is the square root of the sum of the square of each component of the vector gives the magnitude. Let us explain it with an example. Consider a vector A with its components img The magnitude of this vector is, img From this equation, we can conclude that x component of the vector nor the y component of the vector can be greater than the magnitude of the vector.

The airplane moves with the speed v and makes an angle with the horizontal axis. Then the speed of the airplane resolved into horizontal and vertical components. The resolution of the speed of airplane is as shown in the figure. img In the figure, img is the angle made by the speed of the airplane, v is the actual speed of the airplane, img is the horizontal component of speed of the airplane, and img is the vertical component of speed of the airplane. (a) The horizontal component of speed of the airplane is, img From the figure, the horizontal component of speed of the airplane is, img Here, img is the horizontal component of speed of the airplane, v is the actual speed of the airplane, and img is the angle made by the speed of the airplane. Rewrite the equation img for v. img Substitute 200 km/h for img and img for img in the above equation solve for v. img Therefore, the actual speed of the airplane is img . (b) The magnitude of the vertical component of speed of the airplane is, img Here, img is the vertical component of speed of the airplane. Substitute 210 km/h for img and img for img in the equation img and solve for img . img Therefore, the magnitude of the vertical component of speed of the airplane is img .

Consider a velocity vector img in the first quarter of img plane. If this velocity vector made an angle img with positive img axis in counter clockwise direction, the components of velocity along img axis and img axis are shown in the below figure. img From the above figure, img Rearrange the above equation for img as follows: img Similarly, the cosine of the angle from the above figure is, img Rearrange the above equation for img as follows: img From this equation, img component of velocity associated with cosine. Therefore, the correct option is img .

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