Question

i solved a)u=2i and b)r=2t+1/2[-0.4(i) 0,2(j)]

at c) i don t have idea how to solve

At time t = 0, a small boat is at a buoy travelling due east with speed 2 ms−1
. The boat experiences a constant acceleration of (– 0.4i + 0.1j) ms−2
. The unit vectors i and j are
directed east and north respectively.
(a) Write down the initial velocity of the boat.
(b) Find an expression for the displacement of the boat at time t seconds.
(c) By considering the i component of the displacement vector of the boat, find the
time when the boat is due north of the buoy.
(d) Find an expression for the velocity of the boat at time t seconds and hence find the
time when the boat is travelling northeast from the buoy.

Answer 1

(a) v = 2i

(b) r = 2it + (-0.2i+.05j)t^2
(c) we want r to have a zero i component. So,
2t - 0.2t^2 = 0
0.2t (10-t) = 0
t=10

(d) v = 2i + (-.4i+.1j)t
we want the i and j components to be equal, so
2-.4t = .1t
2 = .5t
t = 4