Answer:
The final speed of the lion-gazelle system immediately after the attack is 69.862 kilometers per hour.
Explanation:
Let suppose that lion and Thomson's gazelle are running at constant speed before and after collision and that collision is entirely inelastic. Given the absence of external force, the Principle of Momentum Conservation is applied such that:
Where:
- Linear momentum of the lion, measured in kilograms-meters per second.
- Linear momentum of the Thomson's gazelle, measured in kilograms-meters per second.
- Linear momentum of the lion-Thomson's gazelle, measured in kilograms-meters per second.
After using the definition of momentum, the system is expanded:
Vectorially speaking, the final velocity of the lion-gazelle system is:
Where:
,
- Masses of the lion and the Thomson's gazelle, respectively. Measured in kilograms.
,
,
- Velocities of the lion, Thomson's gazelle and the lion-gazelle system. respectively. Measured in meters per second.
If ,
,
and
, the final velocity of the lion-gazelle system is:
The speed of the system is the magnitude of the velocity vector, which can be found by means of the Pythagorean theorem:
The final speed of the lion-gazelle system immediately after the attack is 69.862 kilometers per hour.
Answer:
<em>a) P(21)=40</em>
<em>b) P max = 60</em>
<em>c) P min = 20</em>
Explanation:
<u>Function Modeling</u>
The blood pressure P is modeled with the equation
Where t is in seconds.
a) We'll find the pressure when t=21 seconds
b) The maximum value will occur when the sine function has a value of 1
c) The minimum pressure will occur when the sine function is at minimum (-1)
Explanation:
The force acting between two masses is given by :
........(1)
Where
G is the universal gravitational constant
are masses
d is the distance between two masses
It is clear from equation (1) that the gravitational attraction between the bodies always increases if the masses of bodies increases and when the separation between masses decreases.
So, the correct answer is "the masses increase, and the distance between the centers of mass decreases". This is because the force of gravitation is directly proportional to the masses and inversely proportional to the separation.
Answer:
coasting down hill on a bicycle
Explanation:
Coasting down the hill on a bicycle is a typical example of how kinetic energy is being transformed to potential energy in a system.
Kinetic energy is the energy due to the motion of a body, it can be derived using the expression below;
K.E = m v²
Potential energy is the energy due to the position of a body. It can be derived using;
P.E = mgh
m is the mass
v is the velocity
g is the acceleration due to gravity
h is the height
Now, at the top of the hill, the potential energy is at the maximum. As the bicycle coasts down the potential energy is converted to kinetic energy.