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. (d) What are the magnitude and direction of its acceleration at the highest point?

Verified step by step guidance

1. Identify the type of motion: The motion described is projectile motion under the influence of gravity. Since air resistance is ignored, the only force acting on the egg is gravity.
2. Understand the acceleration due to gravity: The acceleration due to gravity is constant and acts downward throughout the motion of the egg. It is denoted as 'g' and typically has a value of approximately 9.8 m/s^2 on Earth.
3. Determine the acceleration at the highest point: At the highest point of its trajectory, the vertical component of the egg's velocity becomes zero momentarily. However, the acceleration due to gravity still acts downward.
4. State the magnitude of the acceleration: The magnitude of the acceleration at the highest point is equal to the acceleration due to gravity, g.
5. Specify the direction of the acceleration: The direction of the acceleration at the highest point is vertically downward.

Key Concepts

Acceleration due to Gravity

Acceleration due to gravity is a constant force acting on objects near the Earth's surface, typically denoted as 'g'. It has a value of approximately 9.81 m/s² downward. This force influences the motion of the egg throughout its trajectory, including at its highest point, where it remains subject to this gravitational pull.

Projectile Motion

Projectile motion refers to the motion of an object that is thrown or projected into the air, subject only to the force of gravity. In this scenario, the egg's path can be analyzed as a vertical projectile, where it ascends until it reaches its peak height and then descends. The characteristics of this motion, including time of flight and maximum height, are governed by the initial velocity and gravitational acceleration.

Highest Point of Trajectory

At the highest point of its trajectory, a projectile's vertical velocity becomes zero momentarily before it begins to descend. However, the acceleration due to gravity remains constant at -9.81 m/s² downward. This means that even though the egg's speed is zero at the peak, it is still accelerating downward due to gravity, which is crucial for understanding its subsequent motion.