1. A 75 kg skydiver in free fall is subjected to a horizontal crosswind exerting a velocity of -5 m/s and to a vertical air velocity of -54 m/s.

a. What is the resultant velocity acting on the skydiver? (5 pts)
b. What direction is the resultant velocity acting? (5 pts)

To find the resultant velocity acting on the skydiver, we can use vector addition. The resultant velocity is the vector sum of the horizontal crosswind velocity and the vertical air velocity.

First, let's find the magnitude of the resultant velocity using the Pythagorean theorem:
resultant velocity = √((horizontal velocity)^2 + (vertical velocity)^2)

a. Magnitude of the resultant velocity:
resultant velocity = √((-5 m/s)^2 + (-54 m/s)^2)
resultant velocity = √(25 m^2/s^2 + 2916 m^2/s^2)
resultant velocity = √(2941 m^2/s^2)
resultant velocity ≈ 54.20 m/s

b. To determine the direction of the resultant velocity, we can use trigonometry. We need to find the angle that the resultant velocity vector makes with the horizontal axis.

angle = arctan(vertical velocity / horizontal velocity)

angle = arctan((-54 m/s) / (-5 m/s))
angle = arctan(10.8)
angle ≈ 84.29 degrees

Therefore, the resultant velocity acting on the skydiver is approximately 54.20 m/s at an angle of approximately 84.29 degrees with the horizontal axis.