Answer: Average Velocity = - 643.42 i + 512.66 j m/s
Magnitude = 822.7 m/s
Direction = 141.45°
Explanation:
r = 3.84 x 10^8 m
w = 2.46 x 10^-6 rad/s
Formula for Average velocity = displacement / time
at t = 0
x(0) = r
y(0) = 0
at t = 8.45 days
= 8.45 x 24 x 3600 s =730080 sec
w t = 2.46 x 10^-6 x 730080 = 1.80 rad Or 102.90°
xf = r cos(w t) = - 0.2233r
yf = r sin(w t) = 0.9747r
Displacement = (xf - x0)i + (yf - y0)j = -1.2233r i + 0.9747r j
<v> = dispalcement / t = (-1.2233r i + 0.9747r j ) / (730080 s )
= - 643.42 i + 512.66 j m/s
Magnitude
= sqrt(643.42^2 + 512.66^2)
= 822.7 m/s
Direction
= 180 - tan^-1(512.66 / 643.42)
= 141.45°
We can answer this using one of the equations of linear
motion:
v = d / t
where:
v = velocity
d = distance
t = time
<span>In the problem, we are asked to find for the time in
which Driver B will catch up to Driver A. Therefore, find the time when dA = dB. Rearranging the
equation and equation dA and dB will result in:</span>
<span>vA * tA = vB * tB
---> 1</span>
It was given that:
vA = 68 mph
tA = tB + 3 (since person A was travelling 3 hours
earlier)
vB = 85 mph
tB = unknown
Substituting into equation 1:
68 * (tB + 3) = 85 * tB
68 tB + 204 = 85 tB
tB = 12 hrs
Therefore driver B would catch up to driver A after 12
hrs.
<span> </span>
