Physics help #2 ?

Question

If both the mass and the velocity of a ball were tripled, the kinetic energy of the ball would increase by a factor of________?
a. 3
b. 6
c. 9
d. 27

Why?

Answer 1

lets pretend its KE is 1J

KE=1/2mv^2

if the mass tripple, its KE is triple: 1x3
if the velocity is triple, its KE go up 9 times: (3)^2 = 9

1x3x9 = 27J

Answer 2

The kinetic energy would increase by a factor of three to the power of three, or 3x3x3 = 27. This is because the mass of the ball is not only tripled, but it is also travelling three times faster.

If only the mass of the ball was tripled, but its velocity remained the same, the KE would only increase by a factor of 3 (or conversely if only the velocity of the ball was tripled and the mass remained the same).
Considering both variables have changed by the same factor of 3, the answer is a function of the cube of the rate of change.

Answer 3

The correct answer would be 27....Reasons are:

When you triple the mass you triple the energy so therefore multiply times 3

When you triple the velocity you increase the energy 3 x 3 = 9 times. If you doubled the velocity the energy would be 2 x 2, etc.

Multiply 3 times for the mass energy increase and 9 times for the velocity energy increase and the correct answer is 27. 3 x 9 = 27

Answer 4

d. 27

1/2*m*v^2 is the original kinetic energy
1/2*3m*(3v)^2 = 1/2*3m*9v^2 = 27(1/2*m*v^2)

Answer 5

KE1=1/2 MV^2

M=3M
V=3V

KE2=1/2(3M)(3V)^2= 1/2(3M)(9V^2) = 27*1/2*MV^2 = 27*KE1

D is correct