A 75 kg person and a 200 kg crate are each parachuted to earth from a plane. Which statement is correct?
a. the crate will reach terminal velocity last, but hit the ground first
b. the person will reach terminal velocity last, but hit the ground first.
c. the person and crate reach terminal velocity at the same time and hit the ground at the same time
d. The person and crate reach terminal velocity at the same time but the crate will hit the ground first.
To answer this question, we need to understand the concept of terminal velocity and its relationship to mass and gravitational force.
Terminal velocity is the maximum velocity an object can attain when falling through a fluid, such as air. It occurs when the force of gravity pulling the object downwards is completely balanced by the drag force acting in the opposite direction.
In this scenario, both the person and the crate are falling through the same fluid (air).
According to Newton's second law of motion, the force on an object is equal to its mass multiplied by its acceleration. The acceleration experienced by an object falling through a fluid is given by the equation F = ma, where F is the force of gravity acting on the object (mg), and 'm' is the mass of the object.
Since the force of gravity acting on the person is less than the force of gravity acting on the crate (due to the difference in mass), the person will experience a smaller force of gravity. Consequently, the person's acceleration will be lower compared to the crate.
Now, let's analyze each statement to find the correct answer based on this understanding:
a. The crate will reach terminal velocity last but hit the ground first. This statement is incorrect because the larger mass of the crate means it will experience a greater gravitational force and reach terminal velocity faster.
b. The person will reach terminal velocity last but hit the ground first. This statement is also incorrect because the person's lower mass results in a smaller gravitational force, allowing them to reach terminal velocity faster than the crate.
c. The person and crate will reach terminal velocity at the same time and hit the ground at the same time. This statement is also incorrect because the person's lower mass allows them to reach terminal velocity before the crate.
d. The person and crate reach terminal velocity at the same time, but the crate will hit the ground first. This is the correct answer. Although both objects reach terminal velocity at the same time, the greater mass of the crate results in a higher force of gravity and thus a higher acceleration. This higher acceleration allows the crate to reach the ground first, despite both objects having reached terminal velocity.
Therefore, the correct answer is d. The person and crate reach terminal velocity at the same time, but the crate will hit the ground first.