Projectile Motion Notes

Projectile Motion Summary

Key Concepts

• Projectile velocity has horizontal and vertical components.

• Free fall concepts apply to vertical motion.

• Horizontal velocity is constant.

• Vertical velocity changes due to gravity.

• Minimum velocity occurs at maximum height where vertical velocity is zero.

• Time to go up equals time to go down to the same level.

• Horizontal displacement is Range; vertical displacement is Height.

• Projectile: The object being thrown.

• Trajectory: The path taken by the projectile.

• If projected horizontally, initial vertical velocity is zero.

• Maximum range is achieved at a projection angle of 45°. Maximum height is achieved at 90°.

• Complementary angles of projection result in the same range (e.g., 15° and 75°).

Synthesis Questions & Answers

• Initial conditions: Angle = 50°, Initial horizontal velocity = 80$m/s, Initial vertical velocity$ v= 98m/s, Time to reach max height = 10 s.

  • Horizontal velocity at maximum height: $v_{x} = 80$ m/s.

  • Vertical velocity at maximum height: $v_{y} = 0$ m/s.

  • Final horizontal velocity: $v_{fx} = 80$ m/s.

  • Final vertical velocity: $v_{fy} = -98$ m/s.

  • Total time in air: t = 20 s.

  • Another angle for the same range: 40°.

  • Angle for greatest height: 90°.

  • Angle for longest range: 45°.

  • Horizontal acceleration: $a_{x} = 0$ m/s².

  • Vertical acceleration: $a_{y} = -9.8$ m/s².