Textbook Question
If a flea can jump straight up to a height of m, what is its initial speed as it leaves the ground?
1
views
Ch 02: Motion Along a Straight Line
Young & Freedman Calc14th EditionUniversity PhysicsISBN: 9780321973610
Not the one you use?Change textbookSelect a different textbook
Table of contents
- Ch 01: Units, Physical Quantities & Vectors41
- Ch 02: Motion Along a Straight Line67
- Ch 03: Motion in Two or Three Dimensions47
- Ch 04: Newton's Laws of Motion23
- Ch 05: Applying Newton's Laws59
- Ch 06: Work & Kinetic Energy14
- Ch 07: Potential Energy & Conservation8
- Ch 08: Momentum, Impulse, and Collisions18
- Ch 09: Rotation of Rigid Bodies42
- Ch 10: Dynamics of Rotational Motion48
- Ch 11: Equilibrium & Elasticity27
- Ch 12: Fluid Mechanics31
- Ch 13: Gravitation35
- Ch 14: Periodic Motion32
- Ch 15: Mechanical Waves25
- Ch 16: Sound & Hearing32
- Ch 17: Temperature and Heat36
- Ch 18: Thermal Properties of Matter38
- Ch 19: The First Law of Thermodynamics33
- Ch 20: The Second Law of Thermodynamics22
- Ch 21: Electric Charge and Electric Field36
- Ch 22: Gauss' Law24
- Ch 23: Electric Potential31
- Ch 24: Capacitance and Dielectrics18
- Ch 25: Current, Resistance, and EMF26
- Ch 26: Direct-Current Circuits30
- Ch 27: Magnetic Field and Magnetic Forces18
- Ch 28: Sources of Magnetic Field10
- Ch 29: Electromagnetic Induction28
- Ch 30: Inductance17
- Ch 31: Alternating Current21
- Ch 32: Electromagnetic Waves1
- Ch 33: The Nature and Propagation of Light20
- Ch 34: Geometric Optics34
- Ch 35: Interference19
- Ch 36: Diffraction25
- Ch 37: Special Relativity20
- Ch 38: Photons: Light Waves Behaving as Particles15
- Ch 39: Particles Behaving as Waves26
- Ch 40: Quantum Mechanics I: Wave Functions21
- Ch 41: Quantum Mechanics II: Atomic Structure25
- Ch 42: Molecules and Condensed Matter18
- Ch 43: Nuclear Physics16
- Ch 44: Particle Physics and Cosmology23
Young & Freedman Calc14th EditionUniversity PhysicsISBN: 9780321973610Not the one you use?Change textbook
Chapter 2, Problem 35b
If a flea can jump straight up to a height of m, How long is it in the air?
Verified step by step guidance1
Identify the known values: the maximum height (h) the flea can reach is 0.440 m, and the acceleration due to gravity (g) is approximately 9.81 m/s² downward.
Use the kinematic equation for vertical motion to find the time to reach the maximum height: \( v_f = v_i + a t \), where \( v_f \) is the final velocity (0 m/s at the top), \( v_i \) is the initial velocity, \( a \) is the acceleration (-9.81 m/s²), and \( t \) is the time to reach the maximum height.
Rearrange the equation to solve for the initial velocity \( v_i \): \( v_i = v_f - a t \). Since \( v_f = 0 \) at the maximum height, \( v_i = -(-9.81) t \).
Use another kinematic equation to relate the initial velocity to the maximum height: \( h = v_i t + \frac{1}{2} a t^2 \). Substitute \( v_i \) from the previous step and solve for \( t \).
The total time the flea is in the air is twice the time to reach the maximum height, as the time to ascend and descend are equal. Calculate the total time using \( t_{total} = 2t \).
Verified video answer for a similar problem:
This video solution was recommended by our tutors as helpful for the problem above.
Video duration:
4mWas this helpful?
Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Projectile Motion
Projectile motion refers to the motion of an object thrown or projected into the air, subject to only the acceleration of gravity. In this context, the flea's jump can be analyzed as a vertical projectile motion, where the initial velocity, maximum height, and time of flight are key parameters.
Recommended video:
Guided course
04:44
Introduction to Projectile Motion
Kinematic Equations
Kinematic equations describe the motion of objects under constant acceleration. For vertical motion, the equation h = v_i * t + 0.5 * g * t^2 can be used, where h is the height, v_i is the initial velocity, g is the acceleration due to gravity, and t is the time. These equations help determine the time the flea is in the air.
Recommended video:
Guided course
08:25Kinematics Equations
Acceleration Due to Gravity
The acceleration due to gravity (g) is approximately 9.81 m/s² on Earth. It acts downward, affecting the motion of all objects in free fall. Understanding this constant is crucial for calculating the time of flight and other parameters in projectile motion problems, such as the flea's jump.
Recommended video:
Guided course
05:20Acceleration Due to Gravity
Related Practice
Textbook Question
A small rock is thrown vertically upward with a speed of m/s from the edge of the roof of a -m-tall building. The rock doesn't hit the building on its way back down and lands on the street below. Ignore air resistance. What is the speed of the rock just before it hits the street?
1
views
Textbook Question
A small rock is thrown vertically upward with a speed of m/s from the edge of the roof of a -m-tall building. The rock doesn't hit the building on its way back down and lands on the street below. Ignore air resistance. How much time elapses from when the rock is thrown until it hits the street?
1
views
Textbook Question
A juggler throws a bowling pin straight up with an initial speed of m/s. How much time elapses until the bowling pin returns to the juggler's hand?
1
views
Textbook Question
At the instant the traffic light turns green, a car that has been waiting at an intersection starts ahead with a constant acceleration of m/s2. At the same instant a truck, traveling with a constant speed of m/s, overtakes and passes the car. How fast is the car traveling when it overtakes the truck?
2
views
Textbook Question
At the instant the traffic light turns green, a car that has been waiting at an intersection starts ahead with a constant acceleration of m/s2. At the same instant a truck, traveling with a constant speed of m/s, overtakes and passes the car. How far beyond its starting point does the car overtake the truck?
2
views