**Physics Problem: Skiing Spy**A spy is escaping by skiing downhill inclined at an angle of $30^\circ$. The spy's speed is 16.5 m/s when she leaves the hill. The hill is 100.0 m above ground level. Air resistance is neglected.**Questions:**a. Does the spy make it across the canyon? Show clearly why or why not.b. Find the magnitude of the spy’s speed when she reaches ground level.**Diagram Explanation:**- The diagram illustrates a skier descending a 30-degree incline.- The initial velocity ($v_0$) of the skier is marked.- The hill's height is indicated as 100 meters.- There's a horizontal distance of 60 meters across a canyon.- The skier's path is depicted with an arrow showing the slope and direction of motion.- The diagram is noted as "not to scale," indicating approximate representation.

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Description: **Physics Problem: Skiing Spy**A spy is escaping by skiing downhill inclined at an angle of $30^\circ$. The spy's speed is 16.5 m/s when she leaves the hill. The hill is 100.0 m above ground level. Air resistance is neglected.**Questions:**a. Does

Answered: Does the spy make it across the canyon?…

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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**Physics Problem: Skiing Spy**

A spy is escaping by skiing downhill inclined at an angle of $30^\circ$. The spy's speed is 16.5 m/s when she leaves the hill. The hill is 100.0 m above ground level. Air resistance is neglected.

**Questions:**

a. Does the spy make it across the canyon? Show clearly why or why not.

b. Find the magnitude of the spy’s speed when she reaches ground level.

**Diagram Explanation:**

- The diagram illustrates a skier descending a 30-degree incline.
- The initial velocity ($v_0$) of the skier is marked.
- The hill's height is indicated as 100 meters.
- There's a horizontal distance of 60 meters across a canyon.
- The skier's path is depicted with an arrow showing the slope and direction of motion.
- The diagram is noted as "not to scale," indicating approximate representation.

Expert Solution

Step 1

Velocity is resolved as follows:

Here the given value of v = 16.5 m/s

Part a.

Velocity $v \sin (30^{\circ})$ will be used for vertical distance.

Time taken to cover vertical distance will be calculated as follows:

$S = u t + \frac{1}{2} a t^{2} 100 = v \sin (30^{\circ}) t + \frac{1}{2} \times 9.8 \times t^{2} 100 = 16.5 \times \frac{1}{2} \times t + \frac{1}{2} \times 9.8 \times t^{2} 9.8 t^{2} + 16.5 t - 200 = 0 t = 3.75 s$

In this time horizontal distance covered will be given as follows:

$D = v \cos (30^{\circ}) \times t D = 16.5 \times \frac{\sqrt{3}}{2} \times 3.75 D = 53.585 m$

During the fall horizontal distance (D) covered is less than 60 m therefore spy cannot make it the across the canyon.

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