At a particular instant, a hot air balloon is 100 m in the air and descending at a constant speed of 2.0 m/s. At this exact instant, a girl throws a ball horizontally, relative to herself, with an initial speed of 28 m/s. When she lands, where will she find the ball? Ignore air resistance.



To solve this problem, we need to consider the motion of the ball in both horizontal and vertical directions, as the motion in each direction is independent of the other. The girl is 100 meters high, so we’ll use kinematic equations to analyze the situation.

### Vertical Motion
In the vertical direction, the initial velocity of the ball (relative to the ground) is the same as the velocity of the balloon, since the ball is thrown horizontally. This means the initial vertical velocity is \(-2.0 \, \text{m/s}\), where the negative sign indicates downward motion.

We can use the following kinematic equation to determine how long it takes the ball to reach the ground:

\[
y = v_{0y}t + \frac{1}{2} g t^2
\]

Where:
- \( y \) is the vertical displacement (\( y = -100 \, \text{m} \), since the ball falls 100 meters down),
- \( v_{0y} \) is the initial vertical velocity of the ball (\( v_{0y} = -2.0 \, \text{m/s} \)),
- \( g \) is the acceleration due to gravity (\( g = 9.8 \, \text{m/s}^2

At a particular instant, a hot air balloon is 100 m in the air and descending at a constant speed of 2.0 m/s. At this exact instant, a girl throws a ball horizontally, relative to herself, with an initial speed of 28 m/s. When she lands, where will she find the ball? Ignore air resistance.

Explore the kinematics of a ball thrown horizontally from a descending hot air balloon 100 meters in the air. Learn how to calculate where the ball will land using principles of projectile motion. The problem covers key concepts such as independent horizontal and vertical motion, and uses kinematic equations. Suitable for students in Grades 10-12.

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