Three students formulate position-time equations to solve Problem 51 on page 55

Question

Three students formulate position-time equations to solve Problem 51 on page 55 of the text. Each uses a different coordinate system (real world position of origin, choice of +/- direction defined by direction of y axis) to describe the motion depicted in the problem statement and formulates an equation describing the position of the ball using the coordinate y. Student 1: y(t) = 8.00 m/s t + 1/2 gt^2 Student 2: y(t) = 30.0 m - 8.00 m/s t - 1/2 gt^2 Student 3: y(t) = -8.00 m/s t - 1/2 gt^2 The equations are based on the general form: y(t) = y_1 + v_1 t + 1/2at^2 and all three formulations are "correct". In each equation g=+9.8 m/s^2 and the initial conditions (t=0) describe a ball 30.0 m from the surface, moving downward at 8.00 m/s. Which of the diagrams below did each student base his or her equation on? Explain your reasoning. b) Each student solves for the t value at which the ball reaches the ground by setting y equal to the position of the ground in his or her chosen coordinate system. What value of y does each student use? Use student 3's formulation (and coordinate system) and solve for the t value just as the ball reaches the ground. That is. solve the problem with student #3's formulation

Explanation / Answer

a)

student 1 ----> 3rd diagram

student 2 ----> 1st diagram

student 3 ----> 2nd diagram

b)

student 1 uses y = 0 m

stduent 2 uses y = -30 m

student 3 uses y = +30 m

c)

y(t) = -8*t - (1/2)*g*t^2

-30 = -8*t - (1/2)*9.8*t^2

on solving the above equation w eget

t = 1.79 s

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