Two bicyclists in a sprint race begin from rest and accelerate away from the origin of an xy coordinate system. Miguel's acceleration is given by
(−0.800i + 1.20j) m/s2,
and Lance's acceleration is given by
(1.40i + 0.400j) m/s2.
(a) What is Miguel's acceleration with respect to Lance? (Express your answer in vector form.)
(aM)L
=
m/s2
(b) What is Miguel's speed with respect to Lance after 3.00 s have elapsed?
m/s
(c) What is the distance separating Miguel and Lance after 3.00 s have elapsed?
m
(a)
subtract M - L
-2.2 i + 0.8 j
(b)relative velocity = -2.2 t i +0.8 t j
if t = 3
v = -6.6 i + 2.4 j
speed = sqrt(6.6*2+2.4^2)
(c) relative position
= -2.2/2 t^2 i + 0.8/2 t^2 j
= -1.1 t^2 i + 0.4 t^2 j
put in 3 for t again and do the square root thing again
To find Miguel's acceleration with respect to Lance, we need to subtract Lance's acceleration from Miguel's acceleration:
(aM)L = (aM) - (aL)
Given:
(aM) = (-0.800i + 1.20j) m/s^2
(aL) = (1.40i + 0.400j) m/s^2
Therefore,
(aM)L = (-0.800i + 1.20j) - (1.40i + 0.400j)
= (-0.800i + 1.20j) - (1.40i + 0.400j)
= -0.800i + 1.20j - 1.40i - 0.400j
= (-0.800 - 1.40)i + (1.20 - 0.400)j
= -2.20i + 0.80j
So, Miguel's acceleration with respect to Lance is (-2.20i + 0.80j) m/s^2.
To find Miguel's speed with respect to Lance after 3.00 s, we can use the equation:
vM/L = (aM)L * t
Given:
(aM)L = (-2.20i + 0.80j) m/s^2
t = 3.00 s
Therefore,
vM/L = (-2.20i + 0.80j) * 3.00
= -2.20 * 3.00i + 0.80 * 3.00j
= -6.60i + 2.40j
So, Miguel's speed with respect to Lance after 3.00 s is (-6.60i + 2.40j) m/s.
To find the distance separating Miguel and Lance after 3.00 s, we can use the equation:
d = (1/2) * (aM)L * t^2
Given:
(aM)L = (-2.20i + 0.80j) m/s^2
t = 3.00 s
Therefore,
d = (1/2) * (-2.20i + 0.80j) * (3.00)^2
= (1/2) * (-2.20i + 0.80j) * 9.00
= (1/2) * (-19.80i + 7.20j)
= -9.90i + 3.60j
So, the distance separating Miguel and Lance after 3.00 s is (-9.90i + 3.60j) m.