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Applications of Velocity and Acceleration in Free Falling Objects

Explore the concepts of velocity, acceleration, and rate of change in free falling objects. Calculate the height, velocity, and speed of a rock launched upwards with a velocity of 160 ft/sec. Understand how to determine acceleration during the rock's flight. Solve for the time when the rock hits the ground and analyze the fall of a ball bearing released from rest, calculating its distance, velocity, speed, and acceleration after 2 seconds.

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Applications of Velocity and Acceleration in Free Falling Objects

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  1. Other Applications of Velocity, Acceleration 2.2b

  2. Rate of Change (see attached sheet)

  3. Free Falling Objects Time Initial Position Gravity -32 for feet -9.8 for meters Initial Velocity

  4. Free Falling Objects Acceleration = derivative of velocity Velocity = derivative of position

  5. A dynamite blast blows a heavy rock straight up with a launch velocity of 160 ft/sec. How high does the rock go? What are the velocity and speed of the rock when it is 256 ft. above the ground on the way up? On the way down? First we need s(t) We want velocity when s(t)=256 Highest point is the maximum. This occurs when v = 0 Speed is the absolute value of velocity, so the speed is 96 ft/sec

  6. What is the acceleration at any time t during its flight? The acceleration is always -32 When does the rock hit the ground again? Rock hits when s(t)=0

  7. Free Fall A heavy ball bearing is released from rest at time t = 0 seconds How many meters does the ball fall in the first 2 seconds? Initial velocity is 0 since we are starting from rest. Initial height is 0 since we are tracking the distance the object falls What is the velocity, speed and acceleration at this time? Speed = 19.6

  8. 2.2b HOMEWORK Pg. 117; #93-96

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