Understanding Kinematics in Free Fall Problems
Kinematics is a branch of physics that deals with the study of the motion of objects without considering the forces that cause the motion. In the context of free fall problems, kinematics helps us understand the motion of objects under the sole influence of gravity. Free fall problems are a fundamental aspect of physics, and solving them requires a thorough understanding of kinematic concepts such as displacement, velocity, acceleration, and time.
In this article, we will solve five essential kinematics free fall problems to help you understand how to apply kinematic concepts to real-world problems. We will use the following kinematic equations to solve these problems:
- v = v0 + at (equation 1)
- s = s0 + v0t + (1⁄2)at^2 (equation 2)
- v^2 = v0^2 + 2a(s - s0) (equation 3)
where: * v = final velocity * v0 = initial velocity * a = acceleration (which is -9.8 m/s^2 for free fall problems) * t = time * s = displacement * s0 = initial displacement
Problem 1: Object Dropped from Rest
An object is dropped from rest at a height of 20 m above the ground. Find its velocity and displacement after 2 seconds.
📝 Note: Since the object is dropped from rest, its initial velocity (v0) is 0 m/s.
Using equation 1, we can find the final velocity (v) after 2 seconds:
v = v0 + at = 0 + (-9.8 m/s^2)(2 s) = -19.6 m/s
The negative sign indicates that the velocity is downward.
Using equation 2, we can find the displacement (s) after 2 seconds:
s = s0 + v0t + (1⁄2)at^2 = 0 + 0 + (1⁄2)(-9.8 m/s^2)(2 s)^2 = -19.6 m
The negative sign indicates that the displacement is downward.
Problem 2: Object Thrown Downward
An object is thrown downward from a height of 30 m with an initial velocity of 10 m/s. Find its velocity and displacement after 3 seconds.
Using equation 1, we can find the final velocity (v) after 3 seconds:
v = v0 + at = 10 m/s + (-9.8 m/s^2)(3 s) = -17.4 m/s
The negative sign indicates that the velocity is downward.
Using equation 2, we can find the displacement (s) after 3 seconds:
s = s0 + v0t + (1⁄2)at^2 = 0 + (10 m/s)(3 s) + (1⁄2)(-9.8 m/s^2)(3 s)^2 = -43.8 m
The negative sign indicates that the displacement is downward.
Problem 3: Object Dropped from a Moving Vehicle
An object is dropped from a moving vehicle that is traveling at a speed of 20 m/s. If the object is dropped from a height of 15 m, find its velocity and displacement after 2 seconds.
📝 Note: Since the object is dropped from a moving vehicle, its initial velocity (v0) is 20 m/s.
Using equation 1, we can find the final velocity (v) after 2 seconds:
v = v0 + at = 20 m/s + (-9.8 m/s^2)(2 s) = 0.4 m/s
The positive sign indicates that the velocity is upward.
Using equation 2, we can find the displacement (s) after 2 seconds:
s = s0 + v0t + (1⁄2)at^2 = 0 + (20 m/s)(2 s) + (1⁄2)(-9.8 m/s^2)(2 s)^2 = 18.4 m
The positive sign indicates that the displacement is upward.
Problem 4: Object Thrown Upward
An object is thrown upward from the ground with an initial velocity of 25 m/s. Find its velocity and displacement after 4 seconds.
Using equation 1, we can find the final velocity (v) after 4 seconds:
v = v0 + at = 25 m/s + (-9.8 m/s^2)(4 s) = -13.2 m/s
The negative sign indicates that the velocity is downward.
Using equation 2, we can find the displacement (s) after 4 seconds:
s = s0 + v0t + (1⁄2)at^2 = 0 + (25 m/s)(4 s) + (1⁄2)(-9.8 m/s^2)(4 s)^2 = 22.4 m
The positive sign indicates that the displacement is upward.
Problem 5: Object Dropped from a Height with Air Resistance
An object is dropped from a height of 40 m. If air resistance is considered, the acceleration of the object is reduced to 6 m/s^2. Find its velocity and displacement after 5 seconds.
Using equation 1, we can find the final velocity (v) after 5 seconds:
v = v0 + at = 0 + (-6 m/s^2)(5 s) = -30 m/s
The negative sign indicates that the velocity is downward.
Using equation 2, we can find the displacement (s) after 5 seconds:
s = s0 + v0t + (1⁄2)at^2 = 0 + 0 + (1⁄2)(-6 m/s^2)(5 s)^2 = -75 m
The negative sign indicates that the displacement is downward.
In conclusion, solving kinematics free fall problems requires a thorough understanding of kinematic concepts such as displacement, velocity, acceleration, and time. By applying the kinematic equations, we can solve a variety of problems involving objects in free fall.
What is kinematics?
+Kinematics is the branch of physics that deals with the study of the motion of objects without considering the forces that cause the motion.
What is free fall?
+Free fall is the motion of an object under the sole influence of gravity, where the object is falling freely without any external forces acting on it.
What are the kinematic equations?
+The kinematic equations are a set of equations that describe the motion of an object in terms of its displacement, velocity, acceleration, and time. The three main kinematic equations are: v = v0 + at, s = s0 + v0t + (1⁄2)at^2, and v^2 = v0^2 + 2a(s - s0).
Related Terms:
- 1-d kinematics answer key pdf
- aplusphysics kinematics-free fall answers
- 1D Kinematics Homework Coursera answers
- 1D Kinematics Worksheet
