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Answer :
The final speed of the lion–gazelle system immediately after the attack is about 65.9 km/hr
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Further explanation
Newton's second law of motion states that the resultant force applied to an object is directly proportional to the mass and acceleration of the object.
[tex]\large {\boxed {F = ma }[/tex]
F = Force ( Newton )
m = Object's Mass ( kg )
a = Acceleration ( m )
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[tex]\large {\boxed {F = \Delta (mv) \div t }[/tex]
F = Force ( Newton )
m = Object's Mass ( kg )
v = Velocity of Object ( m/s )
t = Time Taken ( s )
Let us now tackle the problem !
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Given:
mass of lion = m₁ = 169 kg
velocity of lion = v₁ = 77.3 j km/hr
mass of gazelle = m₂ = 31.7 kg
velocity of gazelle = v₂ = 63.8 i km/hr
Asked:
final speed = v = ?
Solution:
We will use Conservation of Momentum to solve the problem as follows:
[tex]p_1 + p_2 = p[/tex]
[tex]m_1 v_1 + m_2 v_2 = ( m_1 + m_2 ) \overrightarrow{v}[/tex]
[tex]169 ( 77.3 \widehat{j} ) + 31.7 ( 63.8 \widehat{i} ) = ( 169 + 31.7 ) \overrightarrow{v}[/tex]
[tex]\overrightarrow{v} \approx 65.1 \widehat{j} + 10.1 \widehat{i}[/tex]
[tex]|\overrightarrow{v}| \approx \sqrt{65.1^2 + 10.1^2}[/tex]
[tex]|\overrightarrow{v}| \approx 65.9 \texttt{ km/hr}[/tex]
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Learn more
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- The Acceleration Due To Gravity : https://brainly.com/question/4189441
- Newton's Law of Motion: https://brainly.com/question/10431582
- Example of Newton's Law: https://brainly.com/question/498822
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Answer details
Grade: High School
Subject: Physics
Chapter: Dynamics
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Answer: 75,242.9 m/s
Explanation:
from the question we are given the following parameters
mass of Lion (ML) = 169,169 kg
velocity of lion (VL) = 777,377.7 m/s
mass of Gazelle (Mg) = 31,731.7 kg
velocity of Gazelle (Vg) = 63,863.8 kg
mass of Lion and Gazelle (M) = 200,900.7 kg
velocity of Lion and Gazelle (V) = ?
The first figure below shows the motion of the Lion and Gazelle with their direction.
The second diagram shows the motion of the Lion and Gazelle with their directions rearranged to form a right angle triangle.
from the triangle formed we can get the velocity of the Lion and Gazelle immediately after collision using their momentum and Phytaghoras theorem
momentum = mass x velocity
momentum of the Lion = 169,169 x 77,377.3 = 13,089,840,463.7 kgm/s
momentum of the Gazelle = 31,731.7 x 63,863.8 = 2,026,506,942.46 kgm/s
momentum of the Lion and Gazelle = 200,900.7 x V
now applying Phytaghoras theorem we have
13,089,840,463.7 + 2,026,506,942.46 = 200,900.7 x V
15,116,347,406.16 = 200,900.7 x V
V = 75,242.9 m/s
