Question

Exercise 3.4 The position of a squimel running in a 3.6 Previous Answers Request Answer Part D .74 Previous Answs Request Anser Units

Answer 1

Given that,

Position of squirrel, r = (0.28t + 0.036t²) i + 0.019t³ j

(C)

Position of squirrel at 5.45 s,

r = (0.28*5.45 + 0.036*5.45²) i + 0.019*5.45³ j

r = 2.595 i + 3.075 j

Distance of squirrel from initial position at 5.45,

r = sqrt [(2.595)^2 + (3.075)^2]

r = 4.024 m

(D)

velocity vector at 5.45 s,

v = dr / dt

v = d [(0.28t + 0.036t²) i + 0.019t³ j] / dt

v = (0.28 + 0.072t) i + 0.057t² j

v = (0.28 + 0.072*5.45) i + 0.057*5.45² j

v = 0.672 i + 1.693 j

magnitude of velocity,

v = sqrt [(0.672)² + (1.693)²]

v = 1.82 m/s

(E)

Direction of squirrel's velocity,

tan $\theta$ = vy / vx = 1.693 / 0.672

$\theta$ = 68.35 deg