Law of Gravitation- Find an expression for the magnitude of the initial velocity that a projectile must possess in order to leave the earth when air friction is neglected.
The gravitational constant for g is, G = 6.67428*10^-11 m^3 Kg^-1 s^-2
Please answer the question fully and please give any helpful websites, thankyou.
Also I know calculus.
To find the expression for the magnitude of the initial velocity that a projectile must possess to leave the earth when air friction is neglected, we can use the concept of gravitational potential energy and kinetic energy.
The initial velocity required for the projectile to leave the Earth can be calculated by equating the gravitational potential energy at the surface of the Earth to the kinetic energy of the projectile.
The gravitational potential energy (PE) is given by the formula:
PE = mgh
Where:
m = mass of the projectile
g = acceleration due to gravity
h = height from the surface of the Earth
The kinetic energy (KE) of the projectile is given by the formula:
KE = (1/2)mv^2
Where:
m = mass of the projectile
v = velocity of the projectile
We can set the gravitational potential energy equal to the kinetic energy:
mgh = (1/2)mv^2
Mass (m) cancels out on both sides of the equation:
gh = (1/2)v^2
Simplifying the equation:
v^2 = 2gh
Taking the square root of both sides gives us:
v = √(2gh)
Therefore, the expression for the magnitude of the initial velocity (v) that a projectile must possess to leave the Earth when air friction is neglected is:
v = √(2gh)
Note: The height from the surface of the Earth (h) would vary depending on the starting point of the projectile.
As for helpful websites, you may refer to the following resources to further understand the concept of projectile motion and the law of gravitation:
1. Khan Academy: https://www.khanacademy.org/science/physics/two-dimensional-motion
2. Physics Classroom: http://www.physicsclassroom.com/class/vectors/u3l2c.cfm
These websites offer comprehensive explanations, examples, and practice problems to enhance your understanding of the topic.