A large boulder is ejected vertically upward from a volcano with an initial speed of 40.0 m/s. Ignore air resistance. (d) When is the velocity of the boulder zero?

Verified step by step guidance

1. Identify the initial velocity (v_0) of the boulder, which is given as 40.0 m/s.
2. Recognize that the velocity of the boulder will be zero at its highest point, where it momentarily stops before starting to fall back down.
3. Use the kinematic equation for velocity, which is v = v_0 + at, where 'v' is the final velocity, 'v_0' is the initial velocity, 'a' is the acceleration due to gravity (which is approximately -9.8 m/s^2 on Earth), and 't' is the time.
4. Set the final velocity 'v' to zero (0 m/s) because we are looking for the time when the boulder stops moving upward. This gives the equation 0 = 40.0 m/s - 9.8 m/s^2 * t.
5. Solve the equation for 't' to find the time at which the velocity of the boulder is zero.

Key Concepts

Kinematics

Kinematics is the branch of physics that describes the motion of objects without considering the forces that cause the motion. It involves concepts such as displacement, velocity, acceleration, and time. In this scenario, kinematic equations can be used to analyze the boulder's motion as it travels upward and then downward.

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 moving upward, gravity acts in the opposite direction, decelerating the object until it reaches its peak height, where its velocity becomes zero.

Peak Height

The peak height is the maximum altitude reached by an object in projectile motion before it starts descending. At this point, the object's velocity is zero, marking the transition from upward to downward motion. Understanding when the boulder reaches this height is crucial for determining when its velocity becomes zero.