Vertical Motion Problems

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Vertical Motion Problems

• MA.912.A.7.8 Use quadratic equations to solve
  real-world problems.

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Vertical Motion Formuladrt 5t2

• The formula drt (Distance rate X time) works
  when the rate is constant.
• When something is thrown upward into the air, the
  rate varies.
• The rate gets slower and slower as the object
  goes up, then becomes negative as it comes back
  down again.

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drt 5t2

• t is the number of seconds since the object was
  thrown upward.
• d is its distance in meters above where it was
  thrown.
• r is the initial upward velocity in meters per
  second. (The rate when the object was first
  thrown.)

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drt 5t2
Maximum Height
Object
distance
Ground
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• A football is kicked into the air with an initial
  upward velocity of 25 m/sec.
• Write the related equation.
• Calculate the height after 2 sec 3 sec

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Graph

• Clink on link for graphing calculator.
• http//my.hrw.com/math06_07/nsmedia/tools/Graph_Ca
  lculator/graphCalc.html

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• A football is kicked into the air with an initial
  upward velocity of 25 m/sec.
• c. When will it be 20 meters above the
• ground?

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• A football is kicked into the air with an initial
  upward velocity of 25 m/sec.
• d. When will the ball hit the ground?

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• 2. Suppose that you throw a rock into the air
  from the top of a cliff. The initial upward
  velocity is 15 m/sec.
• Write the related
• equation.

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• 2. Suppose that you throw a rock into the air
  from the top of a cliff. The initial upward
  velocity is 15 m/sec.
• b. How high will the rock be above the cliff
  after 2 sec? Where will it be after 4 sec?

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• 2. Suppose that you throw a rock into the air
  from the top of a cliff. The initial upward
  velocity is 15 m/sec.
• c. When will it again be at the same level you
  threw it?

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• 2. Suppose that you throw a rock into the air
  from the top of a cliff. The initial upward
  velocity is 15 m/sec.
• d. When will it hit the water, 50 meters below
  where you threw it?

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• 3. A basketball player shoots a long shot. The
  ball has an initial upward velocity of 6 m/sec.
  When it is released, the ball is at the same
  level as the basket which is 3 meters above the
  gym floor.
• Write the related
• equation.

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• 3. A basketball player shoots a long shot. The
  ball has an initial upward velocity of 6 m/sec.
  When it is released, the ball is at the same
  level as the basket which is 3 meters above the
  gym floor.
• b. After 0.3 seconds, how high is the ball above
  the basket? How high above the gym floor.

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• 3. A basketball player shoots a long shot. The
  ball has an initial upward velocity of 6 m/sec.
  When it is released, the ball is at the same
  level as the basket which is 3 meters above the
  gym floor.
• c. Assuming that the aim is good, when will the
  ball go in the basket.

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• 3.
• c. At what time does the ball reach its highest
  point? How high is the ball above the gym floor?

Time when it goes In the basket.
Time Thrown
The ball reaches its highest point halfway
between the time it is thrown and the time it
reaches the basket.
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• 3.
• c. At what time does the ball reach its highest
  point? How high is the ball above the gym floor?

The ball reaches its highest point halfway
between the time it is thrown and the time it
reaches the basket.