**Lion-Gazelle System Speed and Direction Analysis**Lions can run at speeds up to approximately 80.0 km/h. A hungry 110 kg lion running northward at top speed attacks and holds onto a 39.0 kg Thomson's gazelle running eastward at 76.0 km/h.**Problem 1: Final Speed Calculation**Find the final speed \( v_f \) of the lion-gazelle system just after the lion attacks.\[ v_f = \_\_\_\_\_\_ \, \text{m/s} \]**Problem 2: Direction Angle Calculation**Find the angle \(\theta\) between the final velocity of the lion-gazelle system and the East axis, with positive angles measured counterclockwise from the East axis.\[ \theta = \_\_\_\_\_\_ \, ^\circ \]To solve these problems, apply the principles of conservation of momentum and vector addition to determine the final speed and direction of the combined mass.

Name: **Lion-Gazelle System Speed and Direction Analysis**Lions can run at
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Description: **Lion-Gazelle System Speed and Direction Analysis**Lions can run at speeds up to approximately 80.0 km/h. A hungry 110 kg lion running northward at top speed attacks and holds onto a 39.0 kg Thomson's gazelle running eastward at 76.0 km/h.**Problem

Given: Speed of the lion, v1=80 km/h=22.22 m/s Speed of the gazelle,v2=76 km/h=21.11 m/s Mass of the lion, m1=110 kg Mass of the gazelle, m2=39 kgSolution: The initial momentum of the lion can be calculated as: P1i=m1v1P1i=110 kg22.22 m/s∴P1i=2444.2 kg m/s Similarly, the initial momentum of the gazelle can be calculated as: P2i=m2v2P2i=39 kg21.112 m/s∴P2i=823.368 kg m/s Now, it is given that the Lion is running northward while the gazelle is running eastward, the angle made between their movement will be θ=90°. Let the resultant momentum be R, it can be given as: R2=P12+P22+2P1P2 cosθR2=P12+P22+2P1P2 cos 90°R=P12+P22 …1 substituting values in equation 1 it can be calculated as: R=P12+P22 R=2444.2 kg m/s2+823.368 kg m/s2∴R=2579.20 kg m/s After the collision, the total mass of the system can be calculated as: M=m1+m2M=110 kg+39 kg∴M=149 kg The resultant velocity of the system can be calculated as: vR=RMvR=2579.20 kg m/s149 kg∴vR=17.31 m/s The angle at which the velocity is directed can be calculated as: θ=tan-180 km/h110 kg76 km/h39 kgθ=tan-12.9689∴θ=71.38°The final speed of the Lion-gazelle system is vR=17.31 m/s directed towards the North-East direction at θ=71.38°.

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Macmillan Learning Lions can run at speeds up to approximately 80.0 km/h. A hungry 110 kg lion running northward at top speed attacks and holds onto a 39.0 kg Thomson's gazelle running eastward at 76.0 km/h. Find the final speed vf of the lion-gazelle system just after the lion attacks. Uf = TOOLS Find tl x10 counterclockwise from the East axis. 0 = elocity of the lion-gazelle system and the East axis, with positive angles measured m/s

Macmillan Learning Lions can run at speeds up to approximately 80.0 km/h. A hungry 110 kg lion running northward at top speed attacks and holds onto a 39.0 kg Thomson's gazelle running eastward at 76.0 km/h. Find the final speed vf of the lion-gazelle system just after the lion attacks. Uf = TOOLS Find tl x10 counterclockwise from the East axis. 0 = elocity of the lion-gazelle system and the East axis, with positive angles measured m/s

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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**Lion-Gazelle System Speed and Direction Analysis**

Lions can run at speeds up to approximately 80.0 km/h. A hungry 110 kg lion running northward at top speed attacks and holds onto a 39.0 kg Thomson's gazelle running eastward at 76.0 km/h.

**Problem 1: Final Speed Calculation**

Find the final speed \( v_f \) of the lion-gazelle system just after the lion attacks.

\[ v_f = \_\_\_\_\_\_ \, \text{m/s} \]

**Problem 2: Direction Angle Calculation**

Find the angle \(\theta\) between the final velocity of the lion-gazelle system and the East axis, with positive angles measured counterclockwise from the East axis.

\[ \theta = \_\_\_\_\_\_ \, ^\circ \]

To solve these problems, apply the principles of conservation of momentum and vector addition to determine the final speed and direction of the combined mass.

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