An engineer simultaneously launches a 1\text{ kg} testing sphere and a 5\text{ kg} testing… — Armed Services Vocational Aptitude Battery (ASVAB)

An engineer simultaneously launches a $1\text{ kg}$ testing sphere and a $5\text{ kg}$ testing sphere vertically upward with the exact same initial velocity. At the precise instant they reach their maximum heights (apexes), which of the following statements accurately describes their vertical accelerations? (Assume $g = 9.8\text{ m/s}^2$ and ignore air resistance).

A
The $5\text{ kg}$ sphere experiences a greater downward acceleration because its heavier weight exerts a stronger pull.
B
Both spheres experience a downward acceleration of $0\text{ m/s}^2$ because they are momentarily stationary.
C
The $1\text{ kg}$ sphere experiences a greater downward acceleration because its smaller mass provides less inertia against gravity.
Both spheres experience a constant downward acceleration of $9.8\text{ m/s}^2$ .Answer

Answer

Both spheres experience a constant downward acceleration of

9.8\text{ m/s}^2

In the absence of air resistance, the acceleration due to gravity (

g

) is constant for all objects, regardless of their mass. When an object reaches its highest point, its velocity is momentarily zero, but the gravitational force continues to pull on it without interruption, causing a constant downward acceleration of

9.8\text{ m/s}^2

Step-by-Step Solution

Analyze the forces acting on the spheres at the apex.

Gravity is the only force acting on both spheres, meaning they are in a continuous state of free fall.

Because air resistance is ignored, gravitational pull is the sole factor determining acceleration throughout the entire flight.

Determine the effect of mass on gravitational acceleration.

The acceleration due to gravity is independent of an object's mass.

Although a heavier object experiences a greater gravitational force (weight), it also has proportionally more inertia (mass). These factors cancel out (

a = F/m

), resulting in the same constant acceleration of

9.8\text{ m/s}^2

for both spheres.

Evaluate the effect of momentary zero velocity on acceleration.

Acceleration remains

9.8\text{ m/s}^2

downward even when vertical velocity is momentarily

0\text{ m/s}

Acceleration is the rate of change of velocity. Gravity continuously changes the upward velocity to a downward velocity, passing through zero without the acceleration itself ever dropping to zero.

Key Concept

Constant Gravitational Acceleration in Free Fall

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