Bob (80 kg) lands with a resultant GRF of 1200 N at an angle of 80 degrees from the horizontal. Round answers to nearest whole number.
What was his vertical acceleration during landing?
Bob (80 kg) lands with a resultant GRF of 1200 N at an angle of 80 degrees from the horizontal. What was his vertical acceleration during landing? If his vertical velocity at initial contact of landing is 3.0 m/s, how much work is required to bring his body to a complete stop? What is the vertical displacement of Bob's center of mass during landing? How high did Bob jump?
Sorry I can't follow this at all.
To determine Bob's vertical acceleration during landing, we can use the concept of vectors and resolve the resultant ground reaction force (GRF) into its vertical and horizontal components.
First, let's find the vertical component of the GRF. We'll use trigonometry and apply the equation:
vertical component = GRF * sin(angle)
Given:
GRF = 1200 N
angle = 80 degrees
Using the equation, we get:
vertical component = 1200 N * sin(80 degrees)
vertical component ≈ 1180.01 N
Now that we have the vertical component of the GRF, we can determine the vertical acceleration using Newton's second law of motion. The equation is:
Force = mass * acceleration
In this case, the gravitational force acting on Bob is given by:
Force = mass * gravitational acceleration
Given:
mass of Bob = 80 kg
gravitational acceleration = 9.8 m/s^2
Substituting the values into the equation, we get:
vertical component = mass * gravitational acceleration
Solving for acceleration, we have:
acceleration = vertical component / mass
acceleration = 1180.01 N / 80 kg
Using a calculator, we calculate the vertical acceleration:
acceleration ≈ 14.75 m/s^2
Therefore, Bob's vertical acceleration during landing is approximately 14.75 m/s^2.