A military hovercraft with a mass of 6,000 \text{ kg} is transporting equipment across a f… — Armed Services Vocational Aptitude Battery (ASVAB)

A military hovercraft with a mass of $6,000 \text{ kg}$ is transporting equipment across a frozen lake. The hovercraft's thrusters generate a forward force of $27,000 \text{ N}$ , while air resistance and surface friction create a combined opposing force of $9,000 \text{ N}$ . What is the forward acceleration of the hovercraft?

$3.0 \text{ m/s}^2$ Answer
B
$4.5 \text{ m/s}^2$
C
$0.3 \text{ m/s}^2$
D
$0.33 \text{ m/s}^2$

Answer

The correct forward acceleration of the hovercraft is

3.0 \text{ m/s}^2

The correct answer accurately determines the net force by subtracting the opposing friction (

9,000 \text{ N}

) from the applied thrust (

27,000 \text{ N}

) to get

18,000 \text{ N}

. Dividing this net force by the mass (

6,000 \text{ kg}

) yields an acceleration of

3.0 \text{ m/s}^2

Step-by-Step Solution

Calculate the net forward force acting on the hovercraft.

F_{net} = 27,000 \text{ N} - 9,000 \text{ N} = 18,000 \text{ N}

Acceleration is determined by the net force, which is the sum of all forces acting on the object. The opposing force must be subtracted from the forward thrust.

Set up Newton's Second Law equation.

F_{net} = m \times a

This formula relates net force, mass, and acceleration.

Rearrange the equation to solve for acceleration and substitute the known values.

a = \frac{18,000 \text{ N}}{6,000 \text{ kg}} = 3.0 \text{ m/s}^2

Dividing the net force by the mass gives the resulting acceleration.

Key Concept

Newton's Second Law states that the acceleration of an object is directly proportional to the net force acting upon it and inversely proportional to its mass (

a = \frac{F_{net}}{m}

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