An object is moving in the xy-plane according to the equations x(t) = 3sin(3t) and y(t) = 4cos(3t). What is the maximum magnitude of the particle's acceleration?
- 1) 5 m/s2
- 2) 15 m/s2
- 3) 30 m/s2
- 4) 36 m/s2 [the accepted answer]
- 5) 45 m/s2
x(t) = Asin(wt + phase constant)
The Attempt at a Solution
So, I know that for each dimension if I take the second derivative of the two position equations I get acceleration, and the maximum acceleration for each of those two is simply A*omega^2.
So that's what I did.
For acceleration in the x-dimension, I get: 3*3^2.
For acceleration in the y-dimension, I get 4*3^2.
Taking the squares of the two acceleration components and then summing them and taking the square root of the sum gives 45, which is what I got. Why do the authors then believe 36 m/sec^2 is the right answer?
Thanks in advance for the input!