**Problem 33: Kinematic Analysis of a Skier on an Icy Patch**A skier is sliding downhill at a speed of 8 m/s when she encounters an icy patch where her skis move freely with negligible friction. The vertical distance from the top of the icy patch to the bottom is 10 meters. Determine the skier's speed at the bottom of the icy patch. Is it necessary to know her mass to solve this problem?**Solution:**To find the speed of the skier at the bottom of the icy patch, we use the principle of conservation of mechanical energy. The energy at the top of the icy patch should be equal to the energy at the bottom:\[ E_{\text{top}} = E_{\text{bottom}} \]At the top of the icy patch:- The skier has kinetic energy due to her initial speed.- The skier has potential energy due to her height above the bottom of the patch.At the bottom of the icy patch:- The skier will have only kinetic energy (potential energy will be zero as the height is zero).Let's denote:- \( v_t \) = speed of skier at the top = 8 m/s- \( h \) = height difference = 10 m- \( v_b \) = speed of skier at the bottom (what we need to find)- \( g \) = acceleration due to gravity = 9.81 m/s²Using the energy conservation equation:\[ K_{\text{top}} + U_{\text{top}} = K_{\text{bottom}} \]\[ \frac{1}{2}mv_t^2 + mgh = \frac{1}{2}mv_b^2 \]Here, \( m \) is the mass of the skier, and it cancels out on both sides of the equation:\[ \frac{1}{2}v_t^2 + gh = \frac{1}{2}v_b^2 \]Solving for \( v_b \):\[ \frac{1}{2}(8)^2 + 9.81 \times 10 = \frac{1}{2}v_b^2 \]\[ \frac{1}{2}(64) + 98.1 = \frac{1}{2}v_b^2 \]\[ 32 + 98.1 = \frac{1}{2}v_b^2 \]\[ 130.

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Description: **Problem 33: Kinematic Analysis of a Skier on an Icy Patch**A skier is sliding downhill at a speed of 8 m/s when she encounters an icy patch where her skis move freely with negligible friction. The vertical distance from the top of the icy patch to

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33. A skier is sliding downhill at 8 m/s when she reaches an the icy patch on which her skis move freely with negligible friction. The difference in altitude between the top of the icy patch and its bottom is 10 m. What is the speed of the skier at the bottom of the icy patch? Do you have to know her mass?

33. A skier is sliding downhill at 8 m/s when she reaches an the icy patch on which her skis move freely with negligible friction. The difference in altitude between the top of the icy patch and its bottom is 10 m. What is the speed of the skier at the bottom of the icy patch? Do you have to know her mass?

College Physics

11th Edition

ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter1: Units, Trigonometry. And Vectors

Section: Chapter Questions

Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...

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