Motion in Two Dimensions?

Question

A fish swimming in a horizontal plane has velocity vi = (4.00 i - 3.00 j) m/s at a point in the ocean whose displacement from a certain rock is ri = (10.0 i + 4.00 j) m. After the fish swims with constant acceleration for 15.0 s, its velocity is v = (16.0 i - 5.00 j) m/s.
Q: What direction of acc with respect to vector i? Where is fish at t=20 s? What direction is ti moving?

Answer 1

a = dv/dt = ((16,-5)-(4,-3))/15 = (12,-2)/15 = (0.8, -0.1333333)
mag(a) = 0.811, angle = -9.462 deg
Assume you mean dir. wrt to ri, not "i".
ri = (10,4)
mag(ri) = 10.770, angle = 21.801
angle(a) - angle(ri) = -31.263 deg
At t=20,
location s = s0 + v0t + at^2/2
= (10,4) + 20*(4,-3) + 200*(0.8, -0.1333333)
velocity v = v0 +at = (4,-3) + 20*(0.8, -0.1333333)
Direction of motion = arctan(vy/vx)
(I'll leave these computations to you)