Free Fall Equation | Problems (With Solutions)

Free Fall Equation

For a free falling object, the distance (h) is equal to half times the product of gravity (g) and the square of time (t). Using the equation of free fall: h = ½ × g t2, the value of distance travelled by a free falling object can be calculated.

Here’s the equation of free fall:

  1. Free fall distance and velocity in terms of time, h = ½ × g t2 and v = g t
  1. Free fall time and velocity in terms of distance, t = √2 h/g and t = √2 g h
  1. Free fall time and distance in terms of velocity, t = v/g and h = v2/2 g

Let’s solve some problems based on this equation, so you’ll get a clear idea.

Free Fall Practice Problems

Problem 1: One feather is allowed to free fall from the top of a building. Calculate the distance travelled by a feather, if the time taken by a feather to reach the ground is 20 s. Also calculate the velocity of a feather. (Take the value of gravitational acceleration, g = 9.81 m/s2)

Solution:

Given data:
Time taken by a feather to reach the ground, t = 20 s
Gravitational acceleration, g = 9.81 m/s2
Distance travelled by a feather, h = ?
Velocity of a feather, v = ?

Using the equation of free fall, (free fall distance in terms of time)
h = ½ × g t2
h = ½ × 9.81 × (20)2
h = ½ × 9.81 × 400
h = 1962 m

Therefore, the distance travelled by a feather is 1962 m.

Using the equation of free fall, (free fall velocity in terms of time)
v = g t
v = 9.81 × 20
v = 196.2 m/s

Therefore, the velocity of a feather is 196.2 m/s.


Problem 2: One ball is allowed to free fall from the top of a tower. In order to reach the ground, a ball has to travel the distance of 600 m. After what time, a ball reaches the ground and what is the velocity of a ball? (Take the value of gravitational acceleration, g = 9.81 m/s2)

Solution:

Given data:
Distance travelled by a ball, h = 600 m
Gravitational acceleration, g = 9.81 m/s2
Time taken by a ball to reach the ground, t = ?
Velocity of a ball, v = ?

Using the equation of free fall, (free fall time in terms of distance)
t = √2 h/g
t = √(2 × 600)/9.81
t = √1200/9.81
t = √122.3241
t = 11.06 s

Therefore, the time taken by a ball to reach the ground is 11.06 s.

Using the equation of free fall, (free fall velocity in terms of distance)
v = √2 g h
v = √2 × 9.81 × 600
v = √11772
v = 108.49 m/s

Therefore, the velocity of a ball is 108.49 m/s.


Problem 3: One small piece of paper is allowed to free fall from the 10th floor of a building. If a piece of paper is falling with the velocity of 26 m/s, then how much time will it take to reach the ground? And what is the distance travelled by a piece of paper? (Take the value of gravitational acceleration, g = 9.81 m/s2)

Solution:

Given data:
Velocity of a piece of paper, v = 26 m/s
Time taken by a piece of paper to reach the ground, t = ?
Distance travelled by a piece of paper, h = ?
Gravitational acceleration, g = 9.81 m/s2

Using the equation of free fall, (free fall time in terms of velocity)
t = v/g
t = 26/9.81
t = 2.65 s

Therefore, the time taken by a piece of paper to reach the ground is 2.65 s.

Using the equation of free fall, (free fall distance in terms of velocity)
h = v2/2 g
h = (26)2/(2 × 9.81)
h = 676/19.62
h = 34.45 m

Therefore, the distance travelled by a piece of paper is 34.45 m.


Problem 4: When one box is allowed to free fall from a tower, it takes 4 s to reach the ground. Calculate the distance travelled by a box. (Take the value of gravitational acceleration, g = 9.81 m/s2)

Solution:

Given data:
Time taken by a box to reach the ground, t = 4 s
Distance travelled by a box, h = ?
Gravitational acceleration, g = 9.81 m/s2

Using the equation of free fall, (free fall distance in terms of time)
h = ½ × g t2
h = ½ × (9.81) × (4)2
h = ½ × 9.81 × 16
h = 78.48 m

Therefore, the distance travelled by a box is 78.48 m.

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