Engineering Mechanics

Step 1: Given values.
- Mass of the insect,
- Distance traveled during take-off,
- Initial speed, (since the insect starts from rest)
- Final speed,
- Gravitational acceleration,
Step 2: Use of kinematic equation to find acceleration.
To find the acceleration during take-off, we use the following kinematic equation: Substituting the known values: Step 3: Using Newton's second law to find the net force.
The net force required for the insect to take off is the sum of the force needed to overcome gravity and the force needed to accelerate. The total force is given by: Substituting the mass and acceleration: Additionally, the force required to overcome gravity is: So, the total net force exerted by the hind legs during take-off is: Final Answer:

Step 1: Understanding the problem.
We are asked to find the distance between the center of mass of the system and particle A. The center of mass of a system of particles is given by the weighted average of the coordinates of the particles: Where and are the mass and coordinates of the -th particle, respectively.
Step 2: Assigning coordinates and masses.
- Particle A:
- Particle B:
- Particle C: (since the height of an equilateral triangle with side length 2 m is )
Step 3: Calculating the center of mass coordinates.
First, calculate and : Step 4: Calculating the distance from A to the center of mass.
The distance from particle A to the center of mass is given by the distance formula: Substituting the values: Final Answer: