Math Problem Statement

Two muscles in the back of the leg pull upward on the Achilles tendon, as shown in Figure. (These muscles are called the medial and lateral heads of the gastrocnemius muscle.) Find the magnitude and direction of the total force on the Achilles tendon that can be accelerated upward in a jump by using just those muscles in one leg.

Solution

The image you've uploaded shows a physics problem involving the forces exerted by the muscles in the back of the leg (gastrocnemius muscles) on the Achilles tendon. It appears to be related to calculating the maximum weight that can be accelerated upward using these muscles, given certain forces and angles.

To assist you further with this problem, here are the key aspects to focus on:

  • The forces are shown as vectors, each labeled as 200 N, applied at angles of 20° and 30° from the vertical.
  • The goal is to find the magnitude and direction of the total force on the Achilles tendon that results from these muscle forces.

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Math Problem Analysis

Mathematical Concepts

Vector Addition
Force Decomposition
Trigonometry

Formulas

Resultant Force = √(F1² + F2² + 2 * F1 * F2 * cos(θ))
Components of Force: Fx = F * cos(θ), Fy = F * sin(θ)

Theorems

Law of Cosines
Vector Addition Theorem

Suitable Grade Level

Grades 9-12