91Ó°ÊÓ

When a basketball referee tosses the ball upwards, he imparts an initial velocity, which is the starting speed of the ball. In our example, the initial velocity is given as

• 4.6 meters per second (m/s).

Initial velocity is a crucial factor in determining how high the ball will go and how long it will take to reach its peak. This initial thrust helps overcome the opposing force of gravity. Once the ball leaves the referee's hand, gravity starts taking over, slowing the ball down until it reaches a momentary pause at the maximum height.
Understanding initial velocity is key because it tells us the starting point of motion calculations. This "push" is what sets the ball into motion upwards, against gravitational pull.

Acceleration due to gravity is a constant force that acts on all objects near the Earth's surface, pulling them downward. This force is represented by

• -9.8 meters per second squared (m/s²).

The negative sign indicates that gravity acts in the opposite direction to the upward motion of the ball.
Once the initial velocity propels the ball upwards, gravity consistently applies its force, slowing the ball down until it stops ascending. At the point where the velocity becomes zero, the ball has reached its maximum height. Understanding gravity is crucial in predicting the ball's movement as it provides the backbone for the equations used in kinematics.

The maximum height is the highest point that the ball reaches before it begins descending. At this point, the velocity of the ball is

• 0 meters per second (m/s).

The forces in play are perfectly balanced, with gravity overcoming the initial upward force.
This concept is important because it is at this peak that transition occurs. We calculate this to understand how long the ball stays in the air before starting to fall. The time to reach the maximum height is half the total time it takes to go up and come back down, owing to the symmetrical nature of projectile motion under constant acceleration.

The kinematic equations are a set of equations that describe how objects move under uniform acceleration. For our current problem, the motion at maximum height is governed by the equation:

• \( v = u + at \)

Where:

• \( v \) is the final velocity (0 m/s at maximum height),
• \( u \) is the initial velocity (4.6 m/s),
• \( a \) is the acceleration (-9.8 m/s²),
• \( t \) is time.

By rearranging the equation to solve for time, we have:

• \( t = \frac{u}{a} = \frac{4.6}{9.8} \approx 0.469 \) seconds.

This calculation explains the time required for the ball to stop moving upwards and start falling down, which is essential for solving problems related to motion.