Question

The kinetic energy K of a moving object varies jointly with its mass m and the square of its velocity v. If an object weighing 40 kilograms with a velocity of 15 meters per second has a kinetic energy of 1000 joules, find the kinetic energy if the velocity is increased to 20 meters per second. Round your answer to two decimal places.

Answer 1

1777.78 Joules

Step-by-step explanation:

v = Velocity of object

m = Mass of object

Kinetic energy

`K=(1)/(2)mv^2\\\Rightarrow m=(2K)/(v^2)\\\Rightarrow m=(2* 1000)/(15^2)`

The mass of the object is 4.44 kg.

Here the mass remains constant

If v = 20 m/s

`K=(1)/(2)mv^2\\\Rightarrow K=(1)/(2)*(2* 1000)/(15^2)* 20^2\\\Rightarrow K=1777.78\ Joules`

The kinetic energy of the object when the speed is increased to 20 m/s is 1777.78 Joules

Answer 2

K' = 1777.777 J

Step-by-step explanation:

Given that

m = 40 kg

v= 15 m/s

K=1000

Given that kinetic energy(K) varies with mass(m) and velocity(v)

K= C(mv²)

Where

C= Constant

m=mass

v=velocity

When

m = 40 kg ,v= 15 m/s ,K=1000

K= C(mv²)

1000 = C( 40 x 15²)

C=0.111111

When m = 40 kg and v= 20 m/s

K' = C(mv²)

K= 0.1111 x (40 x 20²)

K' = 1777.777 J