SPH3U1Lesson 11Kinematics

Acceleration Near Earth’s Surface

Learning Goals

Students will:

  • Use kinematics equations to solve problems related to the vertical motion of objects undergoing acceleration due to gravity.

Preparation at Home

Reading

  • Nelson Physics 11 – Section 1.6 Pg. 40-43 and Tutorial 1 and 2

Interactive Figures

  • Acceleration due to Gravity
  • Free Fall Motion with an Initial Vertical Velocity (Notice the shape of the graphs)

Reading Quiz

Free Fall

Acceleration due to gravity () is the acceleration that occurs when an object is allowed to fall freely. The average value of has been measured to be 9.8 m/s2. Different places on Earth have different values for the acceleration due to gravity. The acceleration due to gravity of an object near Earth’s surface will only be about 9.8 m/s2 if it is dropped through a vacuum. This type of motion is referred to as free fall, where an object falls towards the Earth without experiencing air resistance or other forces affecting its motion.

Sample Problem: Motion of an Object Falling Straight Down

A flowerpot is knocked off a window ledge and accelerates uniformly to the ground. If the window ledge is 10.0 m above the ground and there is no air resistance, how long does it take the flowerpot to reach the ground?

Sample Problem: Motion of an Object Thrown Straight Up

A tennis ball is thrown straight up in the air, leaving the person’s hand with an initial velocity of 3.0 m/s. What is the maximum height above the person’s hand that the ball reaches?

Terminal Velocity

In real-life situations, there will always be air resistance which could have a significant effect on the motion of a falling object. A parachutist can control the amount of air resistance they experience by changing the position of their body. If they dive head first, there will be little air resistance but if they spread their body in a belly flop, they experience a much more significant amount of air resistance.

When the air resistance is equal to the force of gravity acting on the parachutist, the parachutist will stop accelerating and maintain a constant velocity, called the terminal velocity.

In-Class Practice Problems

  1. A kangaroo is capable of jumping to a height of 2.62 m. Determine the takeoff speed of the kangaroo.
  1. If Michael Jordan has a vertical leap of 1.29 m, then what is his takeoff speed and his hang time (total time to move upwards to the peak and then return to the ground)?
  1. A baseball is popped straight up into the air and has a hang-time of 6.25 s. Determine the height to which the ball rises before it reaches its peak. (Hint: the time to rise to the peak is one-half the total hang-time).
  1. Rex Things throws his mother’s crystal vase vertically upwards with an initial velocity of 26.2 m/s. Determine the height to which the vase will rise above its initial height.
  1. A robot probe drops a camera off the rim of a 239 m high cliff on Mars, where the free-fall acceleration is -37 m/s2.
  2. Find the time required for the camera to reach the ground.
  3. Find the velocity with which it hits the ground.
  1. On the moon, a feather is dropped from a height of 1.40 m. The acceleration of gravity on the moon is -1.67 m/s2. Determine the time it takes for the feather to fall to the surface of the moon.
  1. Dionte is riding the Giant Drop at Great America. If Dionte free-falls for 2.6 seconds.
  2. What will be his final velocity?
  3. How far will he fall?
  1. The observation deck of a skyscraper is 420 m above the street. Determine the time required for a penny to free-fall from the deck to the street below.
  1. A baseball is thrown straight up in the air with an initial velocity of 2.0 m/s. Draw a picture that shows the path of the ball as it goes up and comes down. Label the initial velocity, the velocity at maximum height, and the acceleration of the ball.

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