Question

17%) Problem 3: The shadow of a perdulin cast on a 7at board moves on attraight line By placing the x aus on the st wnth the origin at the middle of the total path, the x-coordinate of the shadow is given by the following function x()-52cos(a), where t is in seconds and x is in centimeters edl I ▲25% Part (a) Find the speed, m centimeters per second, of the shadow at 14s. Putethal 100% - coans c atano acotanOsinhO cosho tanhocotanh0 世% per attemp。 Degrees Radians Foback dedtion per feedhack ii ▲ 25% Part (b) Find the speed, in centimeters per second, of the shadow ar t-12 25% Part (c) Find the magnitude of the acceleration, meters per second squared, of the shadow's motion at t-1/ -& 25% Part (d) How much distance, in centimeters, does the shadow travel in 20 sec? 46 5 6 7 8

Answer 1

V = dn/dt = d/dt [52 cos (t) V_t = 1/4 = -52 times pi times sin (pi times 1/4) = -115 51 cm /s rightarrow V = -115 51 cm/s V_t = 1/2 = -52 times pi times sin (pi times 1/2) = -163.36 cm/s rightarrow V = -163.36 cm/s a = dv/dt = d/dt [- 52 pi sin (pi t) = -52 pi^2 times cos (pi t) t = 1/3 = -52 times pi^2 times cos (pi times 1/3) = -256.61 cm/s^2 = -2.56 m/s^2 rightarrow a = -2.56 m/s^2 T = 2 pi/w = 2 pi/h = 2.5 in 2 sec it will a of 4A = 4 times 52 cm = 208 cm in 20 sec it will ravel 208/2 times 20 cm = 2080 cm rightarrow n = 2080 cm