A body of mass 10kg is moving with a velocity (6i +8j) at a certain instant. it's K.E will be. A) 250J B) 500J C)100 J D) 1000J ...?

1 Answer
May 24, 2018

B) 500J

Explanation:

For 2D motion:
# v = v_x# i + #v_y # j

In our case:

# v = 6# i + #8 # j #(ms^-1)#

Now # v^2 = v_x^2+v_y^2 #
This can be seen using Pythagoras on a triangle with hypotenuse #v#, opposite #v_y# and adjacent #v_x# or by taking the dot product of the velocity vector with itself to find its length squared .

& # KE =1/2*mv^2 # (by definition)

so substituting for #v^2# we get

-> #KE =1/2m(v_x^2+v_y^2)#

-> #KE =1/2*10*(6^2+8^2) J# (we are given mass is 10kg)

So plugging into a calculator (or using mental math):

#KE = 500 J #