Question

Proszę rozwiązać to zadanie.

Answer 1

ax=100*cos(5*t)

ay=100*sin(5*t)

tx=π/5 s

vx=∫ax·dt, vx(0)=0

100*∫cos(5t) dt = 20*sin(5t) + C

vx(0)=20*sin(0) + C = 0

-20*sin(0) = C

C=0

vx(t)=20*sin(5t)

x=∫vx·dt, x(0)=0

x=∫20*sin(5t)·dt

x=-4*cos(5t)+C

x(0)=-4*cos(0)+C=0

C=4

x(t)=-4*cos(5t)+4

x(π/5)=-4*cos(π)+4

x(tx)=8 m

vy=∫ay·dt, vy(0)=0

100*∫sin(5t) dt = -20*cos(5t) + C

vy(0)=-20*cos(0) + C = 0

20 = C

vy(t)=-20*cos(5t)+20

y=∫vy·dt, y(0)=0

y=∫(-20*cos(5t)+20)·dt

y=-4 (sin(5t) - 5t) + C

y(0)=-4*(sin(0)-0)+C=0

C=0

y(t)=-4*(sin(5t) - 5t)

y(π/5)=-4*(sin(π) - π)

y(tx)≈12,57 m