What are the velocities of (b) a 75 kg skydiver falling with p = -4100j kg m/s

Verified step by step guidance

1. Identify the given momentum of the skydiver, which is \( p = -4100 \, \text{j} \, \text{kg m/s} \). The negative sign indicates the direction of the momentum vector.
2. Recognize that momentum (p) is the product of mass (m) and velocity (v), expressed by the equation \( p = m \times v \).
3. Substitute the mass of the skydiver into the momentum equation. Given that the mass \( m = 75 \, \text{kg} \), the equation becomes \( -4100 \, \text{j} = 75 \, \text{kg} \times v \).
4. Solve for the velocity (v) by rearranging the equation: \( v = \frac{-4100 \, \text{j}}{75 \, \text{kg}} \).
5. Interpret the result: The negative sign in the velocity indicates the direction of the velocity vector, which is downward in this context.

Key Concepts

Momentum

Momentum is a vector quantity defined as the product of an object's mass and its velocity. It is represented by the equation p = mv, where p is momentum, m is mass, and v is velocity. In the context of the skydiver, the given momentum value indicates the direction and magnitude of the skydiver's motion, which is crucial for understanding their velocity.

Velocity

Velocity is a vector quantity that describes the rate of change of an object's position with respect to time. It includes both speed and direction, making it essential for analyzing motion. In this case, the velocity of the skydiver can be derived from the momentum value provided, allowing us to understand how fast and in which direction the skydiver is falling.

Conservation of Momentum

The conservation of momentum principle states that in a closed system, the total momentum before an event must equal the total momentum after the event, provided no external forces act on it. This concept is important in analyzing the motion of the skydiver, especially when considering interactions with air resistance or other forces during free fall.