We want to find the coefficient of restitution e between the ball and the floor. We will be able to measure the time of flight between subsequent bounces, but not the velocities before and after each impact. Question 1 a. Using the kinematics equation for position, find a relationship between the time of flight tn and the velocity of the ball after the nth bounce. You should obtain a quadratic equation that has two solutions for the time tm, but only one of them represents the time of flight. b. Using the kinematics equation for velocity and the relationship determined in the previous step, find the relationship between the velocity right after the nth bounce and the velocity right before the (n +1)th bounce? c. Given your answers to the previous parts of this question and the definition of €, find the coefficient of restitution e in terms of the subsequent times of flight tn and tr+1.

We want to find the coefficient of restitution e between the ball and the floor. We will be able to measure the time of flight between subsequent bounces, but not the velocities before and after each impact. Question 1 a. Using the kinematics equation for position, find a relationship between the time of flight tn and the velocity of the ball after the nth bounce. You should obtain a quadratic equation that has two solutions for the time tm, but only one of them represents the time of flight. b. Using the kinematics equation for velocity and the relationship determined in the previous step, find the relationship between the velocity right after the nth bounce and the velocity right before the (n +1)th bounce? c. Given your answers to the previous parts of this question and the definition of €, find the coefficient of restitution e in terms of the subsequent times of flight tn and tr+1.

Name: We want to find the coefficient of restitution e between the ball and
Uploaded: 2024-03-05T11:56:34.000Z
Channel: Bartleby
Description: We want to find the coefficient of restitution e between the ball and the floor. We will be able to measure the time offlight between subsequent bounces, but not the velocities before and after each impact.Question 1a. Using the kinematics equation

College Physics

11th Edition

ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter7: Rotational Motion And Gravitation

Section: Chapter Questions

Problem 12CQ: A child is practicing for a BMX race. His speed remains constant as he goes counterclockwise around...

See similar textbooks

Similar questions

I. If s’(t) = v(t), and s’’(t) = a(t), use the fact that integration reverses differentiation (+C) and the given information about s(t) to find the particular solution to the following problem. If a model rocket’s velocity is given by a(t)= -32 m/s2 and v(0)= 10 and position at 1 second is 1,000 m, find s(t). Hint: Integrate a(t) to find v(t), then integratev(t) to find s(t), finding each C using the given info.
The record distance in the sport of throwing cowpats is81.1 m. This record toss was set by Steve Urner of the UnitedStates in 1981. Assuming the initial launch angle was 45°and neglecting air resistance, determine (a) the initial speedof the projectile and (b) the total time the projectile was inflight. (c) Qualitatively, how would the answers change if thelaunch angle were greater than 45°? Explain.
A child is practicing for a BMX race. His speed remains constantas he goes counterclockwise around a level track withtwo nearly straight sections and two nearly semicircular sections,as shown in theaerial view of FigureCQ7.12. (a) What are thedirections of his velocityat points A, B, and C? Foreach point, choose one:north, south, east, west,or nonexistent. (b) Whatare the directions of hisacceleration at points A,B, and C?
Use a graphing utility to generate the trajectory of a paper airplane whose equations of motion for t ≥ 0 arex = t − 2 sin t, y = 3 − 2 cos t Assuming that the plane flies in a room in which the floor is at y = 0, explain why the plane will not crashinto the floor. [For simplicity, ignore the physical size of the plane by treating it as a particle.] How high must the ceiling be to ensure that the plane does not touch or crash into it?
s On October 9, 1992, a 27-pound meteoritestruck a car in Peekskill, NY, leaving a dent 22 cm deep in thetrunk. If the meteorite struck the car with a speed of 130 m>s,what was the magnitude of its deceleration, assuming it to beconstant?
a student stands at the edge of a cliff and throws a stone horizontally with a speed of v0=18.5 m/s. the cliff is h=49.o m above a flat, horizontal beach. (a) what are the coordinates in the initial position of the stone in xo and yo? (b) what are the components of the initial velocity? in vox and voy? (d) write the equations for the position with time, using the coordinates with x and y? (c) write the equations for the x- and y-b components of the velocity? (e) how long after being released does the stone strike the beach below the cliff? (e) with what speed and angle of impact do the stand land?
Clay Matthews, a linebacker for the Green Bay Packers, can reach a speed of 10.0 m/s. At the start of a play, Matthews runs downfield at 45 with respect to the 50-yard line and covers 8.0 m in 1 s. He then fins straight down the field at 90 with respect to the 50-yard line for 12 m, with an elapsed time of 1.2 s. (a) What is Matthews’ final displacement from the start of the play? (b) What is his average velocity?
Check your Understanding A cyclist rides 3 km west and then tune around and tides 2 kin east. (a) What Is his displacement? (b) What is the distance traveled? (c) What is the magnitude of his displacement?
Between t=0 and t=t0 , a rocket moves straight upward with an acceleration given by a(t)=ABt1/2 , where A and B are constants. (a) If x is in meters and t is in seconds, what are the units of A and B ? (b) If the rocket starts from rest, how does the velocity vary between t=0 and t=t0 ? (c) If its initial position is zero, what is the rocket’s position as a function of time during this same time Interval?
A dart is thrown horizontally at a speed of 10 m/s at the bull’s-eye of a dartboard 2.4 m away, as in the following figure. (a) How far below the Intended target does the dart hit? (b) What does your answer tell you about how proficient dart players throw their darts?
A projectile is launched at an angle of 30 and lands 20 s later at the same height as it was launched. (a) What is the initial speed of the projectile? (b) What is the maximum altitude? (c) What is the range? (d) Calculate the displacement from the point of launch to the position on its trajectory at 15 s.
A marble rolls off a tabletop 1.0 m high and hits the floor at a point 3.0 m away from the table’s edge in the horizontal direction. (a) How long is the marble in the air? (b) That is the speed of the marble when it leaves the table’s edge? (c) What is its speed when it hits the floor?