Q1. A small bag of sand is released from an ascending hot air balloon whose constant, upward velocity is 4.25 m/s. If the balloon is 220 m above the ground when the sandbag is released, how much time does it take for the sandbag to reach the ground?

Background

Topic: Kinematics in One Dimension (Vertical Motion)

This question tests your understanding of vertical motion under gravity, specifically how to analyze the motion of an object released from a moving platform. The sandbag starts with an initial upward velocity and then falls under the influence of gravity.

Key Terms and Formulas

• Initial velocity (): The velocity of the sandbag at the moment it is released (upward, 4.25 m/s).

• Initial height (): The height above the ground where the sandbag is released (220 m).

• Acceleration due to gravity (): m/s2, acting downward.

• Time interval (): The time it takes for the sandbag to reach the ground.

• Kinematic equation for vertical displacement:

Since the sandbag lands on the ground, .

Step-by-Step Guidance

1. Identify the known values: m, m/s (upward), m/s2 (downward), and m (ground level).

2. Set up the kinematic equation for vertical motion: .

3. Substitute the known values into the equation: .

4. Rearrange the equation to standard quadratic form: .

5. To solve for , use the quadratic formula: , where , , and .

Try solving on your own before revealing the answer!