FREE FALL PROBLEMS

Equations

a = g = acceleration due to gravity = -10 m/s2 (Actual value is -9.81 m/s2 which makes the 10 m/s2 a good estimate

Δd = viΔT + (1/2)g ΔT2 a = g = ΔV/ ΔT

Δd = vavg ΔT a = vf - vi

ΔT

Instantaneous velocity = gΔT + vivavg = vf + vi

2

Velocity and acceleration have direction since they are vector quantities. Always remember:

  • Down is negative (-) direction and up is (+) direction
  • Initial velocity of a dropped object = 0
  • Object thrown upward – Initial velocity = positive number and final velocity at the top is 0
  • Object thrown up and when it hits the ground the final velocity is same as initial velocity except it is now negative
  • A = g = -10m/s2
  1. How much speed does a freely falling object gain each second?
  1. For a freely falling object dropped from rest, what is its instantaneous speed at the end of the fifth second of fall? The sixth second?
  1. For an object thrown straight upward, what is its instantaneous speed at the top of its path? Its acceleration?
  1. How far will a freely falling object fall from a position of rest in five seconds? In six seconds?
  1. If a freely falling rock were equipped with a speedometer, by how much would its velocity readings increase in m/s each second of the fall?
  1. If a freely falling rock were equipped with an odometer, by how much would its distance readings increase in meters each second of the first 3 seconds of the fall ? Explain your answer
  1. How far will a freely falling object have fallen after 1 sec from a position of rest when its instantaneous speed has reached-10 m/s?

Answer D = -5 m

8. Complete the chart for an object dropped from a 100 meter tower.

Time (s) / Instantaneous Velocity (m/s) / Distance fallen (m)
0
1
2
3

9. Sketch the distance above the ground vs time graph below.

10. Sketch the velocity vs time graph below

  1. Find the velocity required to throw a ball straight up and have it return 6 seconds later. Assume air resistance is zero.

Answer vi = 30 m/s

In problem 11, how high did the ball go?

Answer d = 45 m

  1. King Kong carries Mr. Trautwein up the 321 meter tall EmpireStateBuilding. Traut’s shoe falls off, how fast will the shoe be moving when it hits the ground?

Answer v = -80.1 m/s

  1. A baby birds sits in a tree waiting the arrival of mom with a worm. Too bad the baby bird is a LOSER, the worm misses the nest and falls to the ground in 1.5 s. How high up is the baby bird’s nest?

Answer d =-11.25 m

  1. A giraffe (6 M tall) , bites a branch off a tree. He chews the leaves and drops the branch. (Messy eater!) How long does it take for the branch to fall to the ground?

Answer t = 1.09 s

  1. How long is Tina the Ballerina in the air when she leaps straight up with a speed

of 1.8 m/s?

Answer = .36 s

  1. In order to open the clam it catches, the seagull will drop the clam repeatedly onto a hard surface from high in the air until the shell cracks. If the seagull flies to a height of 25 M, how long will the clam take to fall?

Answer t = 2.24 s

  1. Catch the dollar bill and you can keep it. Hold the mid point of the bill at finger level. Without any advanced warning, drop the bill. If the person can catch it, they can keep it!. Can you beat Physics! Measure the length of a dollar bill. Also, human reaction time (time for nerve impulses to travel from the eye to the brain to the fingers) is rarely less than 1/7 seconds.

Answer = -9.8 cm

  1. Free fall is a ride that carries passengers to a height of 33.5 m and drops them to the ground inside a small cage. How fast are the passengers traveling when they reach the ground?

Answer = -25.8 m/s

  1. Mr. Birzes won the National Biological heaviest teacher award for 2001! He was so excited that he threw his textbook up and out of the third floor H wing which is 30 meters high. It was seen heading up with a speed of 20 m/s. (Lots of times heavy guys are strong!) Fill in the data table below with the velocity of the book.

Time (s) / Velocity (m/s) / Distance above ground (m)
0
1
2
3
4
5
6
7
8
  1. Calculate your reaction time. Have a friend release a ruler while the top of your fingers are at the 0 cm mark. Catch the ruler and read the distance at the top of your fingers. This is the distance the ruler traveled until you grabbed it. Convert centimeters to meters.

Hint d = ½ gt2 Solve for t

  1. An instrument package is dropped from a weather balloon. If the package falls a distance of 100 m, determine:
  1. the time it will take to hit the ground.

Answer t = 4.47 s

  1. the velocity with which it will hit the ground.

Answer v = -44.7 m/s

  1. A baseball popup is hit vertically with an initial velocity of 25 m/s:
  2. Determine the time it will take to reach the maximum height it will achieve.

Answer t = 2.5 s

  1. Determine its maximum height.

Answer 31.25 m

  1. Determine the time it will take to return to the ground.

Answer 2.5 s

  1. Determine the velocity it will hit the ground.

Answer = - 25m/s