Chapter 4, Problem 49A

(a)

To determine

The rank:

The objects (a shot put, an air-filled balloon, and a basketball) in the order in which they reach the terminal velocity when they are thrown simultaneously from the top of a building.

Answer to Problem 49A

The rank of the objects in the order of attainment of the terminal velocity is the air-filled balloon, basketball, and shot put.

Explanation of Solution

Introduction:

Consider an object is dropped from a height; it will experience drag force in the upward direction and gravitational pull in the downward direction.

Initially, the velocity of the object is very small resulting in lesser drag force and predominant gravitational pull.

As the object moves downwards, the velocity of the object increases which in turn increases the drag force.

At a particular time, the drag force becomes equal to the gravitational pull, and the corresponding velocity of the object is known as the terminal velocity of the object.

When the light objects with larger surface areas are falling from a height, the drag force has a significant effect on the motion of the object and reaches the terminal velocity quickly.

When a heavier and compact object is falling from a height, the drag force does not affect the motion of the object and it takes more time to reach the terminal velocity.

Among a shot put, an air-filled balloon, and a basketball falling from the top of the building.

The air-filled balloon is the lightest and hence, it reaches the terminal velocity quickly.

The basketball is lighter and less compact than the shot put, hence, the basketball reaches the terminal velocity quickly in comparison to the shot put.

Conclusion:

Thus, the order of attaining the terminal velocity is air-filled balloon, basketball, and shot put.

(b)

To determine

The rank of the objects (a shot put, an air-filled balloon, and a basketball) in the order in which they reach the ground when they are thrown simultaneously from the top of the building.

Answer to Problem 49A

The rank of the objects in the order of reaching the ground is shot put, basketball, andair-filled balloon.

Explanation of Solution

Introduction:

Heavier the object was thrown from the top of the building, sooner it will reach the ground surface as they experience higher gravitational pull and reaches the ground surface sooner in comparison to lighter objects.

Among a shot put, an air-filled balloon, and a basketball falling from the top of the building,

The shot put is the heaviest object experiencing higher gravitational pull and will reach the ground very soon.

The basketball is a moderate weight object and experiences significant gravitational pull and will reach the ground just after the shot put reaching the ground surface.

The air balloon is the lightest object and experiences the least gravitational pull in comparison to the other two objects. It reaches the ground just after basketball reaching the ground.

Conclusion:

The rank of the objects in the order of reaching the ground is shot put, basketball, andair-filled balloon.

(c)

To determine

The relationship between the answer in part (a) and part (b).

Answer to Problem 49A

The rank the objects in the order of attainment of the terminal velocity in part (a) is inverse of the rank the objects in the order of reaching the ground in part (b).

Explanation of Solution

Introduction:

Consider an object is dropped from a height; it will experience drag force in the upward direction and gravitational pull in the downward direction.

At a particular time, the drag force becomes equal to the gravitational pull, and the corresponding velocity of the object is known as the terminal velocity of the object.

When a heavier the object is thrown from the top of the building, it will reach the ground sooner as they experience higher gravitational pull as compared to the lighter objects.

Compare part (a) and part (b).

The rank of the objects in the order of attainment of the terminal velocity is the air-filled balloon, basketball, and shot put.

The rank of the objects in the order of reaching the ground is shot put, basketball, andair-filled balloon.

Hence, the rank the objects in the order of attainment of the terminal velocity in Part (a) is inverse of the rank the objects in the order of reaching the ground in Part (b).

Conclusion:

Thus, the rank the objects in the order of attainment of the terminal velocity in Part (a) is inverse of the rank the objects in the order of reaching the ground in Part (b).