Math Problem Statement

A person stands at rest on a slope which makes an angle 16 degrees to the horizontal. They have a mass of 73 kg. They start to run up the slope. After a time of 7.4 s they reach a distance 23 m up the slope and have a velocity of 3.0 m/s.

(a) Calculate the vertical height gained.

  select units m kg s m/s m/s^2 N J W degrees none 

(b) Determine how much energy the person has used.

  select units m kg s m/s m/s^2 N J W degrees none 

(c) Calculate the average power output of the person.

Solution

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Math Problem Analysis

Mathematical Concepts

Trigonometry
Kinematics
Work-Energy Principle
Power Calculation

Formulas

Vertical height gained: h = d * sin(θ)
Kinetic energy: KE = 0.5 * m * v^2
Potential energy: PE = m * g * h
Total energy used = PE + KE
Average power output: P = Total energy / time

Theorems

Work-Energy Theorem

Suitable Grade Level

Grades 10-12