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

Verified step by step guidance

1. Identify the type of motion: The boulder is undergoing vertical motion under the influence of gravity, which is a uniformly accelerated motion.
2. Understand that the velocity of the boulder will be zero at the peak of its trajectory. This is the point where the boulder stops ascending and is about to start descending.
3. Use the kinematic equation for velocity in uniformly accelerated motion: $v=v$₀-gt, where $v$ is the final velocity, $v$₀ is the initial velocity, $g$ is the acceleration due to gravity (approximately $9.8 m/s^2$), and $t$ is the time.
4. Set the final velocity $v$ to zero to find the time at which the velocity is zero: $0=40.0-9.8t$.
5. Solve the equation for $t$ to find the time at which the velocity is zero: $t=\frac{40.0}{9.8}$.

Key Concepts

Projectile Motion

Projectile motion refers to the motion of an object thrown or projected into the air, subject to only the acceleration of gravity. In this scenario, the boulder is ejected vertically, and its motion can be analyzed using the principles of projectile motion, focusing on the vertical component.

Initial Velocity

Initial velocity is the speed at which an object begins its motion. For the boulder, the initial velocity is 40.0 m/s upward. This value is crucial for calculating the time it takes for the boulder to reach its peak height, where its velocity becomes zero.

Acceleration due to Gravity

Acceleration due to gravity is the constant rate at which objects accelerate towards the Earth, approximately 9.8 m/s². It acts downward, opposing the boulder's upward motion, and determines how quickly the boulder slows down until its velocity reaches zero at the peak of its trajectory.