An egg is thrown nearly vertically upward from a point near the cornice of a tall building. The egg just misses the cornice on the way down and passes a point 30.0 m below its starting point 5.00 s after it leaves the thrower's hand. Ignore air resistance. (c) What is the magnitude of its velocity at the highest point?

Verified step by step guidance

1. Identify the key information given: The egg is thrown upward and returns to a point 30.0 m below its starting point in 5.00 seconds. The problem asks for the velocity at the highest point.
2. Understand that at the highest point of its trajectory, the vertical component of the velocity of the egg is zero. This is because at the peak of any projectile's path, it momentarily stops moving upward before starting to descend.
3. Recall the kinematic equation for vertical motion without air resistance, which is $v = u + at$. At the highest point, $v = 0$ (where $v$ is the final velocity, $u$ is the initial velocity, and $a$ is the acceleration due to gravity, which is approximately $-9.8 \, \text{m/s}^2$).
4. Use the information that the total time for the trip up and down is 5.00 seconds to find the time to reach the highest point. Since the motion up and down are symmetrical, the time to reach the highest point is half of the total time, which is $2.50$ seconds.
5. Apply the first kinematic equation to find the initial velocity $u$ using $u = v - at$. Substitute $v = 0$, $a = -9.8 \, \text{m/s}^2$, and $t = 2.50 \, \text{s}$ to find $u$. This initial velocity $u$ is also the magnitude of the velocity at the highest point, which is zero.

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, understanding the kinematic equations is essential to analyze the egg's motion as it travels upward and then downward, particularly in determining its velocity at the highest point.

Velocity

Velocity is a vector quantity that refers to the rate at which an object changes its position. It has both magnitude and direction. At the highest point of its trajectory, the egg's vertical velocity becomes zero momentarily before it starts descending, which is a critical aspect to consider when calculating its velocity at that specific point.

Acceleration due to Gravity

Acceleration due to gravity is the acceleration experienced by an object due to the gravitational force exerted by the Earth, approximately 9.81 m/s² downward. This constant acceleration affects the egg's motion throughout its flight, influencing both its upward and downward journey. Understanding this concept is vital for calculating the egg's velocity at the highest point, as it determines how quickly the egg slows down and then accelerates back down.