A large boulder is ejected vertically upward from a volcano with an initial speed of 40.0 m/s. Ignore air resistance. (b) At what time is it moving at 20.0 m/s downward?

Verified step by step guidance

1. Identify the initial velocity (u) of the boulder, which is 40.0 m/s upward. Since the boulder will eventually move downward, the final velocity (v) we are looking for is -20.0 m/s (negative because it is in the opposite direction to the initial velocity).
2. Use the acceleration due to gravity (g), which is approximately 9.8 m/s^2 downward. Remember to consider the direction of gravity relative to the initial velocity. Since they are in opposite directions, the acceleration will be -9.8 m/s^2.
3. Apply the kinematic equation for velocity: v = u + at, where 'v' is the final velocity, 'u' is the initial velocity, 'a' is the acceleration, and 't' is the time. Substitute the known values into the equation.
4. Rearrange the equation to solve for time (t): t = (v - u) / a.
5. Substitute the values into the rearranged equation to find the time at which the boulder is moving at 20.0 m/s downward.

Key Concepts

Kinematics

Kinematics is the branch of mechanics that describes the motion of objects without considering the forces that cause the motion. It involves concepts such as displacement, velocity, and acceleration. In this scenario, we analyze the boulder's vertical motion using kinematic equations to determine its velocity at different times.

Acceleration due to Gravity

Acceleration due to gravity is the rate at which an object accelerates towards the Earth when in free fall, typically denoted as 'g' and approximately equal to 9.81 m/s². For an object thrown upward, gravity acts in the opposite direction, decelerating the object until it reaches its peak height, after which it accelerates downward. This concept is crucial for calculating the boulder's velocity at the specified time.

Velocity

Velocity is a vector quantity that describes the rate of change of an object's position with respect to time, including both speed and direction. In this problem, we need to determine when the boulder's velocity reaches -20.0 m/s (downward), which involves understanding how its velocity changes over time due to the influence of gravity.