JL

Projectile Motion Part II _ Quarter 4 Grade 9 Science Week 2 Lesson(360P)

Introduction to Projectile Motion Launched at an Angle

  • Learning Objective: Investigate the relationship between the angle of release and the height and range of the projectile.

  • Previous Concepts: Basic concepts of projectile motion, including trajectory and definition.

Key Concepts

Definition of Projectile Motion

  • Projectile Motion: A body in projectile motion exhibits a parabolic trajectory consisting of horizontal and vertical components.

Components of Projectile Motion

  • Horizontal Component:

    • Acceleration = 0 (constant velocity).

  • Vertical Component:

    • Constant acceleration due to gravity (9.8 m/s²).

  • Combination: Projectile motion is the combination of horizontal motion (constant velocity) and vertical motion (constant acceleration).

Example of Projectile Motion

  • Example: Baseball hit at an angle.

Analysis of Vertical Velocity (v_y)

  1. Ascent: Vertical velocity (v_y) decreases due to opposing gravitational force.

  2. Maximum Height: At peak (point B), v_y = 0.

  3. Descent: As it returns (point B to C), v_y increases (direction aligns with gravity).

Facts about Projectile Motion Launched at an Angle

  1. Initial Position: A projectile starts from rest at an upward angle (angle θ).

  2. Initial Velocity Components: Resolved into horizontal (v_x) and vertical (v_y) components.

  3. Constant Horizontal Velocity:

    • Horizontal velocity (v_x) remains constant; acceleration = 0.

  4. Time to Stop & Return: Time to ascend to max height equals time to return to launch point.

  5. Velocity Magnitudes: Initial vertical velocity upward matches final vertical velocity when returning to original height.

Projectile Angles and Their Effects

  • Angle of Release:

    • Affects range and height of the projectile.

  • Greatest Range: Achieved at a 45-degree angle.

  • Maximum Height: Achieved at a 75-degree angle.

  • Complementary Angles: 30 degrees and 60 degrees have the same range.

  • Vertical Displacement: Increases with higher launch angles; at maximum height, v_y = 0.

Example Problem: Projectile Launched at an Angle

Problem Situation

  • Baseball: Hit at 25 degrees with a velocity of 30 m/s.

  • Calculate: Maximum height and horizontal displacement.

Given Values

  • Initial Velocity (v_i): 30 m/s

  • Angle (θ): 25 degrees

  • Acceleration Due to Gravity (g): 9.8 m/s²

Calculation of Maximum Height (D_y)

  1. Formula: D_y = (v_i * sin θ)² / (2 * g)

  • Substitute: D_y = (30 * sin 25°)² / (2 * 9.8)

  1. Calculation Steps:

    • Multiply values: 160.745...

    • Divide: 8.20 m (maximum height reached).

Calculation of Horizontal Displacement (D_x)

  1. Find Total Time (T):

    • Formula: T = 2 * (v_i * sin θ) / g

    • Result: T = 2.59 seconds.

  2. Horizontal Displacement Calculation:

    • Formula: D_x = v_i * cos θ * T

    • Final result: D_x = 70.42 m.

Conclusion

  • Summary: The angle of launch significantly impacts the range and height of a projectile.

  • Key Takeaways:

    • 45 degrees for maximum range; 30 and 60 degrees yield the same range; 75 degrees for maximum height.

    • Remember complementary angles and their effect on range.

Closing Remarks

  • Encourage sharing and subscribing for further learning.

  • Shout out to specific students and teachers.