Answer:
(a) [tex]10\hat{i} - 25\hat{j}[/tex] m/s
(b) [tex]50\hat{i} - 75\hat{j}[/tex] m
(c) [tex](2.00\hat{i} - 5.00\hat{j}) m/s^{2}[/tex]
Solution:
As per the solution:
Acceleration of Heather, a = [tex](3.00\hat{i} - 2.00\hat{j})[/tex]
Acceleration of Jill, a' = [tex](1.00\hat{i} + 3.00\hat{j})[/tex]
Time interval, t = 5.00 s
Now,
(a) Heather's velocity, v = at = [tex](3.00\hat{i} - 2.00\hat{j})\times 5.00 = 15\hat{i} - 10\hat{j}[/tex] m/s
Jill's velocity, v' = a't = [tex](1.00\hat{i} + 3.00\hat{j})\times 5.00 = 5\hat{i} + 15\hat{j}[/tex] m/s
Now, speed oh Heather w.r.t Jill = v - v' = [tex](15\hat{i} - 10\hat{j}) - (5\hat{i} + 15\hat{j}) = 10\hat{i} - 25\hat{j}[/tex] m/s
(b) Distance between Heather and Jill:
d = [tex](v - v')t = (10\hat{i} - 25\hat{j})\times 5 = 50\hat{i} - 75\hat{j}[/tex] m
(c) Heather's acceleration w.r.t Jill:
[tex]a_{r} = a - a' = (3.00\hat{i} - 2.00\hat{j}) - (1.00\hat{i} + 3.00\hat{j}) = (2.00\hat{i} - 5.00\hat{j}) m/s^{2}[/tex]
