physics components questions?

Question

hello i am learning how to solve problems in physics using components and i know how to use components generally but this question just makes it a little bit more complicated: here is it and i will really appreciate the help of how to solve it thanks alot

A watercraft with Vi = 6.4 m/s[E] undergoes an average acceleration of 2.0 m/2^2 [s] for 2.5 s. what if Vf of the watercraft?

the answer in the back of the book is 8.1 m/s [E 38 S]

again thanks alot

its not a misprint because this problem is dealing with 2 dimensional vectors

Answer 1

the final E/W velocity = the initial E/W velocity, because there's no acceleration in that direction. Call that vx.

The final N/S velocity is given by:
vy = -1/2 at^2.
I made it minus because N and E are positive. South is negative.

The magnitude of the velocity is given by pythagorus:
v = sqrt (vx^2 + vy^2)
= sqrt (vx^2 + a^2 t^4 / 4)

The direction is given by:
angle = arctan (vy/vx)
= arctan (-at^2 / 2vx)

They give you a, t, and vx. Plugnchug.

Answer 2

Sounds like a misprint in the book.
Vf = Vi + at so
Vf = 6.4 + 2.0 * 2.5 = 11.4 m/s

Doug