During a testing sequence, a heavy torpedo with a mass of 1,500 \text{ kg} is fired from a… — Armed Services Vocational Aptitude Battery (ASVAB)

During a testing sequence, a heavy torpedo with a mass of $1,500 \text{ kg}$ is fired from a submarine tube. The launch mechanism applies a forward propulsive force of $45,000 \text{ N}$ . If the water resistance creates a constant opposing drag force of $9,000 \text{ N}$ , what is the initial acceleration of the torpedo?

Answer: 24 m/s^2

Answer

To find the acceleration, we first determine the net force acting on the torpedo. The forward propulsive force is

45,000 \text{ N}

, but water resistance pushes back with

9,000 \text{ N}

. Subtracting the opposing force gives a net force of

36,000 \text{ N}

. Using Newton's Second Law (

F = ma

), we rearrange the formula to solve for acceleration (

a = \frac{F}{m}

). Dividing the net force (

36,000 \text{ N}

) by the mass (

1,500 \text{ kg}

) results in an acceleration of

24 \text{ m/s}^2

Step-by-Step Solution

Calculate the net force (

F_{net}

) acting on the torpedo.

F_{net} = 45,000 \text{ N} - 9,000 \text{ N} = 36,000 \text{ N}

The torpedo experiences forces in opposite directions, so the drag force must be subtracted from the forward thrust to find the total effective force.

Calculate the acceleration (

a

) using Newton's Second Law.

a = \frac{F_{net}}{m} = \frac{36,000 \text{ N}}{1,500 \text{ kg}} = 24 \text{ m/s}^2

Newton's Second Law states that acceleration equals the net force divided by the mass.

Key Concept

Newton's Second Law (F=ma) and Net Force

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