Lecture on Ball Toss Motion

Introduction

• Discussion on the motion of a ball when it is tossed upwards.
• Initial conditions:
  • Ball is thrown from a height of 1 meter.
  • Initial velocity of the ball is 10 m/s.
  • Gravity (g) = 9.8 m/s².

Key Concepts

Motion When Thrown Upwards

• Velocity decreases as the ball ascends.
• At the peak, the velocity is 0 but acceleration is still downward.
• Acceleration is always downward.

Motion When Falling Down

• Velocity and acceleration are in the same direction (downward), causing velocity to increase.

Equations and Calculations

• Equation: v² = v₀² - 2gh
  • Used to find the maximum height reached by the ball.
  • Final velocity v at peak = 0 m/s.
  • Initial velocity v₀ = 10 m/s.
  • Solved height (h) from throw to peak is 5.1 meters.
  • Total height from ground to peak = 6.1 meters.

Time to Reach Peak

• Equation: v = v₀ - gt
  • Solved time to reach peak (A to P) = 1.02 seconds.

Descent Time

• Time from peak (P) back to initial height (B) is 1.02 seconds due to symmetry (ignoring air resistance).

Total Time in Air

• Total time from initial height back to same height: 2.04 seconds (A to P to B).

Speed at Initial Height (B)

• Speed at the returning point (B) without air resistance is the same as initial throw speed: 10 m/s.

Total Time to Reach Ground

• Equation: h = v₀t + ½gt²
  • Total time from peak (P) to ground (G) = 1.12 seconds.
  • Total air time from initial throw to ground = 2.14 seconds.

Speed Upon Hitting Ground

• Equation: v = √(2gh)
  • Speed upon impact with ground = 10.93 m/s (greater than initial throw speed due to downward acceleration).

Conclusion

• Summary of the motion characteristics of a tossed ball.
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