A particle rotates counterclockwise in a circle of radius 3.00 m with a constant angular speed of 8.00 rad/s. At t = 0, the particle has an x coordinate of 2.00 m and is moving to the right. A) Determine the x coordinate as a function of time. B) Find the x components of the particle's velocity and acceleration at any time t.

A woman stands at the edge of a cliff and throws a pebble horizontally over the edge with a speed of v0 = 20.5 m/s.The pebble leaves her hand at a height of h = 55.0 m above level ground at the bottom of the cliff, as shown in the figure. Note the coordinate system in the figure, where the origin is at the bottom of the cliff, directly below where the pebble leaves the hand. Answer parts a-f.

VCM-2 As Khanh is driving her car along a straight road with a constant speed, she passes over a series of hills and dips. Each dip and hill has a radius of curvature of 250m She has a 5.00kg package sitting on a scale on the seat beside her. On one stretch of the road she passes thru a dip and then over a hill as shown below. a) Use the velocity vectors shown for V1 and V2, the velocities just before and just after the bottom of the dip, to show the direction of AV, the change in velocity in going thru the bottom of the dip. R=250m Car at the top of the hill. Car at the bottom of the dip. V2 b) Apply Fnet-ma to write symbolic equations for the package when it is in the car at the bottom of the dip. Include all forces on the package. If something equals zero, show it here, otherwise use no numbers in this step. R=250m

P In the movie Avengers, Hawkeye fires an arrow with a cable attached to a building after jumping from it to avoid an explosion. If he fires the arrow 5 m away and 8 m below the top of the building, with a velocity of 100 m/s and a slope of 12:5, determine the horizontal distance the arrow will travel from his initial point of firing to the point where it hits the top of the building. Prove using equations of projectile motion that the arrow will not hit the top corner of the building Please provide diagrams too, thank you

3. A small object moves on a circle of radius R = 7.87 m. The speed of the object as a function of time is v = c1*t, where c1 = 4.84 m/s². %3D → t=0 R a. The object starts at t = 0 on the positive x-axis and moves counterclockwise around the circle. When the object has an angle a = counterclockwise, what is the direction of the instantaneous velocity vector (with respect to the positive x-axis, measured counterclockwise)? 16.3 degrees with respect to the positive x-axis, measured b. What is the magnitude of the instantaneous acceleration vector at timet= 1.05s?

Suppose a fast-pitch softball player does a windmill pitch, moving her hand through a circular arc with her arm straight. She releases the ball at a speed of 30.9 m/s (about 69.1 mph). Just before the ball leaves her hand, the ball's radial acceleration is 331 m/s?. What is the length of her arm from the pivot point at her shoulder? m length: