Question

Newton's Satellite Directions: Read the background information and complete the activity Newton's Thought Experiment In the seventeenth century, Sir Isaac Newton was studying the nature of motion and gravity. He formulated a thought experiment that would eventually become the basis of the development of satellites. Imagine an object is fired from a cannon horizontal to the plane of the earth. The projectile will travel in a horizontal direction and undergo projectile motion as gravity begins to pull the projectile downward. However, the earth is a sphere, which means as the projectile travels, the earth's surface will be begin to drop out underneath the projectile. This means the faster the projectile travels, the farther it has to fall in order to hit the ground. Therefore, since scientists know how far a projectile falls every second, and they know the curvature of the earth, they can calculate how far the projectile has to travel in order to have the earth drop off the same amount as the projectile would drop off due to gravity. In other words, if the projectile would travel fast enough so that it would fall toward the earth forever, never getting any closer to the surface. This thought experiment became known as Newton's satellite. Using his knowledge of gravity and kinematics, Newton was able to calculate exactly how fast a projectile must move in order to fall perpetually Your Assignment Like Newton, you will calculate the speed of a projectile to determine how to put an object in orbit. In addition, with your calculations, you will provide a diagram that shows the projectile and how it would move when it becomes a "satellite." Here is the information you require .The projectile's mass is not needed .The projectile must be launched on the horizontal plane The earth drops 8 inches for every mile traveled .The acceleration due to gravity is 9.81 meters per second squared. Ignore air resistance You will have to calculate how far an object drops every second due to gravity

Answer 1

We know, the distance, x = at^2/2 where, a is constant velocity = 9.81 m/s^2 t is the time velocity, V = distance/time = x/t for t = 1 sec and a = 9.81 m/s^2 x = (9.81)(1)^2/2 = 4.9 m x = 4.9 m speed, v = x/t = 4.9/1 = 4.9 m/s V = 4.9 m/s for t = 2 sec, a = 9.81 m/s^2 x = 9.8 (2)^2/2 = 17.6 m (because = at^2/2) Speed, V = x/t = 19.6/2 = 9.8 m/s for t = 3sec x = aT^2/2 = 9.81(3)^2/2 = 44.1 m speed, V = x/t = 44.1/3 = 14.7 m/s V = 14.7 m/s Average acceleration = delta V/delta t = Average velocity = 4.9 + 9.8 + 14.7/3 = 98 m/s the average acceleration = 9.8 m/s/3s = 3.26 m/s^2