Find Final Kinetic Energy of 3.00kg Object

[suppy123]

Homework Statement

A 3.00kg object has velocity 7.00j m/s. Then, a total force 12.0i N acts on the object for 5.00s.
Find the final kinetic energy from 1/2mvf^2 = 1/2mvf . vf

Homework Equations

The Attempt at a Solution

i got 1/2 * 3 * (20i+7j)(20i+7j)
then 600j^2 + 210ij + 73.5j^2

but the answer is 673.5 J, why?
since j.j =i.i=1 and i.j=0?

 

[Kurdt]

You've not done the dot product correctly.

http://mathworld.wolfram.com/DotProduct.html

 

[suppy123]

!? do i need to write the whole of that!??

600j^2 + 210ij + 73.5j^2
600j.j + 210 i . j + 73.5j.j
600(1) + 210 (0) + 73.5(1)
is this alright

 

[Kurdt]

No that's not how a dot product works. You don't expand the brackets.

$$\mathbf{a} \cdot \mathbf{b} = a_xb_x + a_yb_y$$

For vectors:

$$\mathbf{a} = (a_x,a_y)$$
$$\mathbf{b} = (b_x,b_y)$$

 

[suppy123]

No that's not how a dot product works. You don't expand the brackets.

$$\mathbf{a} \cdot \mathbf{b} = a_xb_x + a_yb_y$$

For vectors:

$$\mathbf{a} = (a_x,a_y)$$
$$\mathbf{b} = (b_x,b_y)$$

got it, a.b = axbx+ayby
a.b= 20i*20i+7j*7j= 449

 

[Kurdt]

A dot product gives a scalar answer and that's why it is sometimes called a scalar product. Drop the i's and j's and add the numbers together.