If a flea can jump straight up to a height of 0.4400.440 m, How long is it in the air?

Ch 02: Motion Along a Straight Line

Young & Freedman Calc - University Physics 15th Edition

Young & Freedman Calc15th EditionUniversity PhysicsISBN: 9780135159552Not the one you use?Change textbook

All textbooks

Young & Freedman Calc 15th Edition

Ch 02: Motion Along a Straight Line

Problem 31b

Chapter 2, Problem 31b

If a flea can jump straight up to a height of $0.440$ m, How long is it in the air?

Verified step by step guidance

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:

Was 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.

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.

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

05:20

Acceleration Due to Gravity

Related Practice

Textbook Question

If a flea can jump straight up to a height of $0.440$ m, what is its initial speed as it leaves the ground?

views

Textbook Question

A small rock is thrown vertically upward with a speed of $22.0$ m/s from the edge of the roof of a $30.0$ -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?

views

Textbook Question

A small rock is thrown vertically upward with a speed of $22.0$ m/s from the edge of the roof of a $30.0$ -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?

views

Textbook Question

A small block has constant acceleration as it slides down a frictionless incline. The block is released from rest at the top of the incline, and its speed after it has traveled $6.80$ m to the bottom of the incline is $3.80$ m/s. What is the speed of the block when it is $3.40$ m from the top of the incline?

views

Textbook Question

A cat walks in a straight line, which we shall call the $x$ -axis, with the positive direction to the right. As an observant physicist, you make measurements of this cat's motion and construct a graph of the feline's velocity as a function of time (Fig. E $2.30$ ). Assuming that the cat started at the origin, sketch clear graphs of the cat's acceleration and position as functions of time.

views

Textbook Question

A juggler throws a bowling pin straight up with an initial speed of $8.20$ m/s. How much time elapses until the bowling pin returns to the juggler's hand?

views