A plane flying in a straight line at constant altitude of 2000 m above the ground with a speed of 200m/s drops an object. Explain how the velocity of the object is actually affected by air resistance. Show how the resistivity force of air and velocity of the object varies with time using graphs
When the object is dropped from the plane, it initially shares the same horizontal velocity as the plane, which is 200 m/s. However, the object is affected by air resistance as it falls towards the ground.
Air resistance is a force exerted by the air on a moving object, opposite to the direction of its velocity. The magnitude of the air resistance force depends on factors such as the density of the air, the size and shape of the object, and the object's velocity.
As the object falls, air resistance increases and starts to reduce its velocity. This reduction in velocity will continue until the air resistance force becomes equal to the gravitational force acting on the object (weight). At this point, the object reaches its terminal velocity, where the air resistance force is equal in magnitude to the gravitational force.
To visualize the variation of the resistive force of air and the velocity of the object with time, let's plot the graphs:
- On the y-axis of the first graph, we will have the resistive force of air, and on the x-axis, we will have time. Initially, as the object starts falling, the air resistance force is minimal. However, as time progresses, the force increases.
- On the y-axis of the second graph, we will have the velocity of the object, and on the x-axis, we will again have time. Initially, the object's velocity is 200 m/s since it shares the same velocity as the plane. But as time passes, the velocity decreases due to the increasing air resistance force. As the object approaches the ground, the velocity approaches its terminal velocity, where the air resistance force and the gravitational force are balanced.
Both graphs will show a downward trend: the increase in air resistance force and the decrease in the object's velocity with time. However, it's important to note that the specific shape of the graphs will depend on factors such as the size and shape of the object and the density of the air it encounters during its fall.