Question

Two particles A and B start from rest at x = 0 and move along parallel paths according to xA = 0.17 sin(πt/2) and xB = 0.08t , where xA and xB are in meters and t is in seconds counted from the start. Determine the time t (where t > 0 ) when both particles have the same displacement and calculate this displacement x.

Chapter 2, Practice Problem 2/105 Two particles A and B start from rest at x = 0 and move along parallel paths according to xa = 0.17 sin(nt/2) and Xg = 0.08t, where XA and Xg are in meters and t is in seconds counted from the start. Determine the time t (where t > 0) when both particles have the same displacement and calculate this displacement x. Answers: t = Click if you would like to Show Work for this question: Open Show Work

Answer 1

At a particular time t both the particles will have same displacement i.e.

a = b

So ,

0.17 sin(at/2) = 0.08

Consider a function

f(x) = 0.17sin(72/2) - 0.08.1

then find it roots. I assure that you cannot solve such an equation by hand. You need to know numerical method like Bisection method, Newton Ralphson method etc. to actually numerically solve it. You can do it in MATLAB by fzero or fsolve command. You can guess the roots but you cannot solve it by hand. Here i have plotted f(x) in Desmos for simplicity. You can see root is 1.501. So time at which both have the same displacement is t=1.501 s.

Displacement at t=1.501s is 0.1201 m

0.17 sin( * ) -0.084 (0.806, 0.098) (0,0) (1.501,0) powered by desmos

For that consider the following function,