The Greatest Acceleration a Man Can Give to an Airplane

What is the greatest acceleration the man can give the airplane when pulling the cable at an angle of 6.8° above the horizontal?

Answer:

The greatest acceleration the man can give the airplane, when pulling the cable at an angle of 6.8° above the horizontal, is approximately 0.259 m/s^2.

Understanding the Calculation:

To find the exact numerical values, let's break down the equations and calculations:

  1. Calculate the maximum tension in the cable:

    2. Tension_horizontal = μ * m_man * g * cos(6.8°)

    Given values are: μ = 0.98, m_man = 82 kg, g = 9.8 m/s^2, and the angle = 6.8°

    Plugging in these values, we get:

    Tension_horizontal ≈ 790.275 N

  2. Calculate the maximum acceleration:

    3. a = (Tension_horizontal - μ * m_man * g) / m_man

    Plugging in the calculated tension and values, we get:

    a ≈ 0.259 m/s^2

Therefore, based on the calculations, the greatest acceleration the man can give the airplane when pulling the cable at an angle of 6.8° above the horizontal is approximately 0.259 m/s^2.

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