Answer Happy

I am mostly confused about where the red box is. I understandthat chain rule is being used, but I keep coming up with an answeraround -19
2:07 AM Tue Feb 11 95% Ca 5 TODO O +BO Homework 2 solutions, page 3. 5) I, J Aladybug taking off from a stalk of wheat travels with the following motion for 30.0 seconds (she doesn't change her position in the vertical direction, z): x(t) = 8.00 t-0.150 t2 sin(t/3.00) y(t) = 0.0120 tỷ where the constants are in Si units (meters, seconds). The argument of sin() is in radians. a) On a plot of x position versus y position, plot the motion. b) What is the ladybug's speed and direction (angle counterclockwise from +x) at t = 23.0 s? Give the answers to three significant figures. c) What is the magnitude and direction of the ladybug's acceleration at this time? Draw the directions of the velocity and acceleration vectors on your plot, with their origin at the point of the ladybug's position at 23.0s. a) See picture below. t=0 at the origin. b) v = dx/dt = (8.00 -0.300t sin(t/3.00) - 0.050 12 cos(t/3.00) ) = -5.19 m/s V = dy/dt = (0.036 t') = +19.0 m/s v = sqrt(5.192 + 19.0%) = 19.7 m/s e = atan(19.7/(-5.19)) = 1.828 rad or 104.8° Beware the error in interpretation of the arctangent! This is not the same as atan((-19.7)/5.19)) which is in the 4th quadrant (284.8 degrees, or 180+our answer) c) a = dv/dt = (-0.300 sin(t/3.00) - 0.100t cos(t/3.00) - 0.100t cos(t/3.00) + 0.0166 t sin(t/3.00)) = -0.200 t cos(t/3.00) + (0.0166 t - 0.300) sin(t/3.00) = +7.48 m/s2 a = dv/dt = 0.072 t = +1.66 m/s? a = sqrt( 7.482 + 1.662 ) = 7.66 m/s 0 = atan(1.66/7.48) = 0.218 rad or 12.5° 250 Note that the velocity vector came out to be tangent to the curve, as it MUST, and the acceleration points inward toward the center of curvature (as it must as well). 200 y,meters 50 OLD 0 50 UUUUUUUUUUU 100 150 200 Dashboard Calendar To Do Notifications M Inbox