free fall worksheet with answers pdf

Lemon

3 min read

·

03-02-2025

1

0

Share

This worksheet provides a thorough exploration of free fall, a fundamental concept in physics. Understanding free fall is crucial for grasping more advanced physics topics like projectile motion and Newton's Laws of Motion. This worksheet includes problems ranging from basic calculations to more complex scenarios, all with detailed solutions provided at the end. Whether you're a high school student, a university student brushing up on concepts, or simply someone curious about physics, this resource will help you master free fall.

Understanding Free Fall

Before we dive into the problems, let's refresh our understanding of free fall. Free fall is defined as the motion of an object solely under the influence of gravity. This means that air resistance is negligible. The acceleration due to gravity (often denoted as 'g') is approximately 9.8 m/s² on Earth. This means that the velocity of a freely falling object increases by 9.8 meters per second every second.

Key Concepts:

• Acceleration due to gravity (g): Approximately 9.8 m/s² downwards.
• Initial velocity (v₀): The velocity of the object at the start of the fall. This is often zero if the object is dropped from rest.
• Final velocity (v): The velocity of the object at the end of the fall.
• Time (t): The duration of the fall.
• Displacement (Δy): The vertical distance the object falls. This is often considered positive downwards.

Free Fall Problems and Solutions

Let's tackle some problems to solidify your understanding. Remember to use the appropriate kinematic equations. The equations below are useful in solving these problems; remember to choose the right equation for the given information.

• v = v₀ + gt
• Δy = v₀t + (1/2)gt²
• v² = v₀² + 2gΔy
• Δy = (v + v₀)/2 * t

Problem 1: A ball is dropped from rest from a height of 10 meters. How long does it take to hit the ground?

Solution: We can use the equation Δy = v₀t + (1/2)gt². Since v₀ = 0, the equation simplifies to Δy = (1/2)gt². Solving for 't', we get: t = √(2Δy/g) = √(2 * 10 m / 9.8 m/s²) ≈ 1.43 seconds.

Problem 2: An object is thrown downwards with an initial velocity of 5 m/s. What is its velocity after 2 seconds?

Solution: We'll use the equation v = v₀ + gt. v = 5 m/s + (9.8 m/s²)(2 s) = 24.6 m/s.

Problem 3: A rock is thrown upwards with an initial velocity of 20 m/s. What is its maximum height? (Remember: at the maximum height, the velocity is 0)

Solution: Use the equation v² = v₀² + 2gΔy. Since v = 0 at the maximum height, we have: 0 = (20 m/s)² + 2(-9.8 m/s²)Δy. Solving for Δy, we get: Δy ≈ 20.4 meters. (Note: We use a negative g because the direction of the acceleration is opposite to the initial velocity.)

Problem 4: A skydiver jumps from a plane. Ignoring air resistance, how far will they fall in 5 seconds?

Solution: Using Δy = v₀t + (1/2)gt², and given v₀ = 0, we get: Δy = (1/2)(9.8 m/s²)(5 s)² = 122.5 meters.

Problem 5 (Advanced): Two objects are dropped from the same height, one 1 second after the other. Find the distance between them after another 2 seconds.

Solution: This problem requires understanding the relationship between time and distance in free fall. Let's say the first object falls for 3 seconds (1 second initial delay + 2 seconds). The second object falls for 2 seconds. Calculate the distance fallen for both objects using Δy = (1/2)gt², then find the difference. This will give you the distance between them.

Answers to Problems

Problem 1: Approximately 1.43 seconds

Problem 2: 24.6 m/s

Problem 3: Approximately 20.4 meters

Problem 4: 122.5 meters

Problem 5: Calculate using the method described above.

This worksheet provides a solid foundation for understanding free fall. Remember to practice these types of problems to further improve your grasp of this fundamental concept. Further exploration might include considering the effects of air resistance in more realistic scenarios. This exercise is a stepping stone toward understanding more complex physics concepts.