1-D Kinematics Free Fall Worksheet Answers Explained
Table of Contents :
In the study of physics, particularly when delving into the realm of kinematics, one of the fundamental concepts students often encounter is 1-D Kinematics and, more specifically, the phenomenon of free fall. This topic not only explores the mechanics behind falling objects but also lays a foundational understanding of motion under the influence of gravity. In this article, we will delve deep into 1-D kinematics related to free fall, explain common worksheet problems, and provide answers with detailed explanations.
Understanding Free Fall 🌍
Free fall refers to the motion of an object under the influence of gravitational force only. It occurs when the only force acting on an object is gravity, meaning there are no other forces, such as air resistance, acting against it.
Key Concepts of Free Fall
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Acceleration due to Gravity (g):
- Near the surface of the Earth, every object in free fall accelerates downward at approximately (9.81 , m/s²). This value is denoted as (g).
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Initial Velocity (u):
- The speed at which an object starts its motion. For objects that are simply dropped, the initial velocity is (0 , m/s).
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Final Velocity (v):
- The speed of the object just before it impacts the ground.
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Displacement (s):
- The distance the object travels while in free fall.
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Time of Flight (t):
- The duration for which the object is in free fall.
Key Equations
To solve problems related to free fall, we often use the following equations of motion:
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( v = u + gt )
- This equation relates final velocity, initial velocity, acceleration, and time.
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( s = ut + \frac{1}{2}gt^2 )
- This equation helps us find the displacement when initial velocity is known.
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( v^2 = u^2 + 2gs )
- This equation connects the velocities and displacement without the need for time.
Example Problems and Solutions
Let’s consider some common worksheet problems and their solutions in the context of 1-D kinematics free fall.
Problem 1: Dropping an Object
Question: An object is dropped from a height of (20 , m). How long will it take to hit the ground?
Solution: Here, we have:
- (u = 0 , m/s) (the object is dropped)
- (s = -20 , m) (the displacement is negative since the object is moving down)
- (g = 9.81 , m/s²)
Using the second equation of motion:
[ s = ut + \frac{1}{2}gt^2 ] [ -20 = 0 \cdot t + \frac{1}{2}(9.81)t^2 ] [ -20 = \frac{9.81}{2}t^2 ] [ t^2 = \frac{-20 \cdot 2}{9.81} ] [ t^2 = \frac{-40}{9.81} \approx 4.08 ] [ t \approx \sqrt{4.08} \approx 2.02 , seconds ]
Important Note: The negative sign in displacement indicates downward motion.
Problem 2: Finding Final Velocity
Question: An object falls freely from rest for (3 , seconds). What is its final velocity just before hitting the ground?
Solution:
- (u = 0 , m/s)
- (t = 3 , s)
- (g = 9.81 , m/s²)
Using the first equation of motion:
[ v = u + gt ] [ v = 0 + (9.81)(3) ] [ v \approx 29.43 , m/s ]
Problem 3: Height Calculation
Question: If an object hits the ground with a speed of (15 , m/s), from what height was it dropped?
Solution:
- (u = 0 , m/s)
- (v = 15 , m/s)
- (g = 9.81 , m/s²)
Using the third equation of motion:
[ v^2 = u^2 + 2gs ] [ (15)^2 = 0 + 2(9.81)s ] [ 225 = 19.62s ] [ s = \frac{225}{19.62} \approx 11.48 , m ]
Summary of Key Equations
To summarize the primary equations involved in free fall, here is a handy table:
<table> <tr> <th>Equation</th> <th>Variables</th> <th>Description</th> </tr> <tr> <td>v = u + gt</td> <td>v = final velocity, u = initial velocity, g = acceleration due to gravity, t = time</td> <td>Calculates final velocity after time t</td> </tr> <tr> <td>s = ut + 0.5gt²</td> <td>s = displacement, u = initial velocity, g = acceleration due to gravity, t = time</td> <td>Calculates displacement during time t</td> </tr> <tr> <td>v² = u² + 2gs</td> <td>v = final velocity, u = initial velocity, g = acceleration due to gravity, s = displacement</td> <td>Relates velocity to displacement without time</td> </tr> </table>
Conclusion
Understanding the principles of 1-D kinematics and free fall is crucial for any student pursuing physics. Through careful application of the equations of motion, one can solve a variety of problems related to falling objects, gaining insight into the nature of gravity and motion. As you practice more problems, you will become adept at interpreting the motion of objects in free fall and correctly applying the kinematic equations to arrive at solutions. Remember to always check your work for accuracy, as minor miscalculations can lead to significant errors in physics. Happy learning! 🚀