The path of a gymnast through space can be modeled as the path of a particle...

The path of a gymnast through space can be modeled as the path of a particle at the gymnast's center of mass, as we will study in a later chapter. The components of the displacement of a gymnast's center of mass from the beginning to the end of a certain trajectory are described by the equations xf = 0 + (10.3 m/s)(cos(18.5°))Tf 0.380 m = 0.640 m + (10.3 m/s)(sin(18.5°))Tf − 1 2 (9.80 m/s2)Tf2 where Tf is in seconds and is the time it takes the gymnast to travel from the takeoff site to the landing point. (a) Identify the gymnast's position (in vector notation) at the takeoff point (in m). (Let the x- and y-direction be along the horizontal and vertical direction, respectively.) r = m (b) Identify the vector velocity at the takeoff point. (Enter the magnitude in m/s and the direction in degrees counterclockwise from the +x-axis.) magnitude Incorrect: Your answer is incorrect. Compare generic expressions for either the x or y-components of the position of an object undergoing two-dimensional motion with the analogous expressions given in the statement of the problem. m/s direction ° counterclockwise from the +x-axis (c) How far (in m) did the gymnast land from the takeoff point?

Expert Solution

genius_generous answered 2 years ago

The motion of a human body through space can be modeled as the motion of a...

The motion of a human body through space can be modeled as the motion of a particle at the body's center of mass as we will study in a later chapter. The components of the displacement of an athlete's center of mass from the beginning to the end of a certain jump are described by the equations xf = 0 + (10.8 m/s)(cos 18.5

The proton is not truly a point particle, but can be modeled as a sphere of...

The proton is not truly a point particle, but can be modeled as a sphere of radius approx 1 fm. This is an approximation. Calculate the probability that the electron in the ground state of hydrogen will be found within 1.00000 fm of the center of the proton in the following two ways. Talk about the differences or lack of differences between the two results. a.) Integrate the radial probability density over the appropriate range of radii. b.) Multiply the...

Find the work done by the force field F in moving a particle through the path...

Find the work done by the force field F in moving a particle through the path C. That is, find Where C is the compound path given by r(t)=<t,0,t> from (0,0,0) to (2,0,2) followed by r(t)=<2,t,2> from (2,0,2) to (2,2,2)

A 6.60 −μC particle moves through a region of space where an electric field of magnitude...

A 6.60 −μC particle moves through a region of space where an electric field of magnitude 1350 N/C points in the positive x direction, and a magnetic field of magnitude 1.25 T points in the positive z direction. If the net force acting on the particle is 6.21×10−3 N in the positive x direction, find the components of the particle's velocity. Assume the particle's velocity is in the x-y plane.

The velocity of a particle traveling in a linear path is known to be: v =...

The velocity of a particle traveling in a linear path is known to be: v = ( s ^ 2 )/ 2000 + ( s ^ 4 )/ 2100 where v and s are [m/s] and [m], respectively. Use Riemann sum to determine the time in seconds for the particle to travel from s = 2 m to s = 3m. Use a minimum of ten (10) intervals. Show all work in this worksheet. The technique spoken of in the...

A gymnast is performing a floor routine. In a tumbling run she spins through the air,...

A gymnast is performing a floor routine. In a tumbling run she spins through the air, increasing her angular velocity from 3.00 to 4.10 rev/s while rotating through two-thirds of a revolution. How much time does this maneuver take?

A bicyclist is riding on a path modeled by the function f(x) = 0.07x, where x...

A bicyclist is riding on a path modeled by the function f(x) = 0.07x, where x and f(x) are measured in miles (see figure). Find the rate of change of elevation at x = 5.

Determine the parametric equations of the path of a particle that travels the circle: (x −...

Determine the parametric equations of the path of a particle that travels the circle: (x − 3)2 + (y − 2)2 = 4 on a time interval of 0≤t≤2π A) if the particle makes one full circle starting at the point (5,2) traveling counterclockwise. x(t)=?, y(t)=? B) if the particle makes one full circle starting at the point (3,4) traveling clockwise. x(t)=?, y(t)=? C) if the particle makes one half of a circle starting at the point (5,2) traveling clockwise....

Rockets can be spin-stabilized; that is, they can fly straighter through space if they rotate around...

Rockets can be spin-stabilized; that is, they can fly straighter through space if they rotate around their long axis. Generally, 1 rotation per second is a good angular speed for spin-stabilization. a. Assume the rocket acts like a solid cylinder. The rocket has a mass of 30000 kg (almost all of it fuel) and a radius of 1.00 m. Calculate the angular momentum of the rocket as it spins. Pay attention to units. b. A problem arises because fuels for...

A particle travelS along the circular path from A to B in 1s. If it takeS...

A particle travelS along the circular path from A to B in 1s. If it takeS 3S for it to go from A to C. Determine Its average velocity when it goes from B to C.

Question