A special effects crew is dropping various props into a deep gorge for a movie scene. Assu… — Armed Services Vocational Aptitude Battery (ASVAB)

A special effects crew is dropping various props into a deep gorge for a movie scene. Assuming air resistance is negligible, arrange the following drops in order from the shortest time in the air to the longest time in the air before hitting the bottom.

1A $100\text{ kg}$ iron safe dropped from a height of $5\text{ m}$
2A $2\text{ kg}$ camera dropped from a height of $20\text{ m}$
3A $50\text{ kg}$ sandbag dropped from a height of $45\text{ m}$
4A $10\text{ kg}$ stunt dummy dropped from a height of $80\text{ m}$

Cevap

The correct sequence from shortest to longest fall time is: the 100 kg safe (5 m), the 2 kg camera (20 m), the 50 kg sandbag (45 m), and finally the 10 kg stunt dummy (80 m).

The time an object spends in free fall from rest is determined entirely by the height from which it is dropped, according to the kinematic equation

t = \sqrt{\frac{2d}{g}}

. Because air resistance is negligible in this scenario, the mass of the objects is completely irrelevant. Therefore, arranging the objects from shortest to longest fall time is identical to arranging them from lowest to highest drop height:

5\text{ m}

(safe),

20\text{ m}

(camera),

45\text{ m}

(sandbag), and

80\text{ m}

(dummy).

Adım Adım Çözüm

Identify the relevant formula for the time of free fall from rest.

d = \frac{1}{2}gt^2

, which rearranges to

t = \sqrt{\frac{2d}{g}}

To determine which variables affect the time an object spends in the air.

Analyze the role of mass in the free fall equation.

Mass (

m

) does not appear in the equation.

In the absence of air resistance, all objects accelerate toward Earth at the exact same rate (

g

), regardless of how heavy they are.

Compare the heights from which the objects are dropped.

The heights are

5\text{ m}

20\text{ m}

45\text{ m}

, and

80\text{ m}

Since fall time is entirely dependent on the initial height (

d

), the object dropped from the lowest height hits the ground first.

Order the objects based on their drop heights from shortest to highest.

Safe (

5\text{ m}

) < Camera (

20\text{ m}

) < Sandbag (

45\text{ m}

) < Dummy (

80\text{ m}

A shorter fall distance results in a shorter amount of time spent in the air.

Anahtar Kavram

In a vacuum or when air resistance is negligible, the acceleration due to gravity is constant for all objects. Therefore, the time it takes to fall depends only on the initial height, not the mass.

Soru

Cevap

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