Final answer:
The mass of the grinch is approximately 16.26 kg.
Step-by-step explanation:
The grinch's energy can be expressed as the sum of kinetic energy and gravitational potential energy. In this case, the energy of the grinch is given as 1000J, which represents the sum of both types of energy. We can calculate the gravitational potential energy using the formula mgh, where m is the mass, g is the acceleration due to gravity, and h is the height. From the given information, we know that the grinch is moving down a hill at 5m/s and has an energy of 1000J. Since the grinch is moving, we can assume that its initial gravitational potential energy is zero. Therefore, we can set up the equation 0 + (1/2)mv^2 + mgh = 1000J, where v is the velocity and h is the height of the hill.
Using this equation, we can solve for the mass of the grinch. Let's consider the height of the hill as h = 5m. We can plug in the given values and solve for m:
0 + (1/2)(m)(5^2) + m(9.8)(5) = 1000J
Simplifying the equation, we get:
0 + (1/2)(25m) + 49m = 1000J
Multiplying through by 2 to eliminate the fraction:
0 + 25m + 98m = 2000J
Combining like terms:
123m = 2000J
Dividing both sides by 123 to solve for m:
m = 2000J / 123 ≈ 16.26kg
Therefore, the mass of the grinch is approximately 16.26 kg.