The vertical motion of mass A is defined by the relation x=10sin(2t)+15cos(2t)+1

Question

The vertical motion of mass A is defined by the relation x=10sin(2t)+15cos(2t)+100. Determine (a) the position, velocity, and acceleration of A when t=1 , (b) the maximum velocity and acceleration of A I only need to find Vmax and Amax. The other guy that answered didn't explain and got the answer wrong.

Explanation / Answer

x=10sin(2t)+15cos(2t)+100 v=x'=20cos(2t)-30sin(2t) a=v'=-40sin(2t)-60cos(2t) a) x at t=1, x(1) = 10 sin 2 + 15 cos 2 + 100 v(1) = 20 cos 2 - 30 sin 2 a(1) = -40 sin 2 - 60 cos 2 b) for Vmax , a=0 , therefore, -2sin(2t)=3cos(2t) => tan(2t)= -1.5 => t = -28.154966237010135 Vmax is at t=-28.154966237010135 Vmax = 36.0555127546398 Answer...... for Amax, a' = 0 a' = -80cos(2t)+120sin(2t) therefore, 2cos(2t)=3sin(2t) => tan(2t)=2/3 => t = 16.845 Amax is at t= 16.845 Amax = -72.11102550923 ...Answer

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