Question

Problem 1a- Consider the kinetic energy of a 17500-kg truck moving at 92.5 km/h and that of an 87.5-kg astronaut in orbit moving at 25500 km/h.

question 1a- What is the ratio of the kinetic energy of the truck to the kinetic energy of the astronaut?

Answer 1

The ratio of the kinetic energy of the truck to the kinetic energy of the astronaut is approximately 218.8. This means that the kinetic energy of the truck is about 218.8 times greater than the kinetic energy of the astronaut.

Step-by-step explanation:

To compare the kinetic energy of the truck and the astronaut, we need to use the formula for kinetic energy:

Kinetic Energy = 1/2 * mass * velocity^2

For the truck, the mass is 17500 kg and the velocity is 92.5 km/h. For the astronaut, the mass is 87.5 kg and the velocity is 25500 km/h. By plugging in these values into the formula, we can calculate the kinetic energy for each. Then, we can find the ratio of the two kinetic energies by dividing the truck's kinetic energy by the astronaut's kinetic energy.

The ratio of the kinetic energy of the truck to the kinetic energy of the astronaut is approximately 218.8. This means that the kinetic energy of the truck is about 218.8 times greater than the kinetic energy of the astronaut.

Answer 2

The ratio of the kinetic energy of the truck to the kinetic energy of the astronaut is 1 : 380.

How to calculate the ratio of the kinetic energy?

The ratio of the kinetic energy of the truck to the kinetic energy of the astronaut is calculated by applying the following formula as follows;

The kinetic energy of the truck is;

K.E = ¹/₂mv²

where;

• m is the mass of the truck, m = 17,500 kg
• v is the speed of the truck, v = 92.5 km/h = 25.7 m/s

K.E = ¹/₂ x 17,500 x (25.7)²

K.E = 5,779,287.5 J

The kinetic energy of the astronaut is;

K.E = ¹/₂mv²

The velocity of the astronaut = 25500 km/h = 7,083.33 m/s

K.E = ¹/₂ x 87.5 x (7,083.33)²

K.E = 2,195,093,420 J

The ratio of the kinetic energy is;

= 5,779,287.5 J / 2,195,093,420 J

= 1 : 380