Questions: Astronaut 1 has a mass of 60 kg. Astronaut 2 has a mass of 80 kg. Astro 1 and 2 want to travel to separate planets, but they want to experience the same weight (in N). Astro 1 visits a planet with gravitational acceleration 7.0 m/s^2. What must be Astro 2 planet's ag to equal Astro 1's weight? Express your answer with the appropriate units.

Solution Steps

To find the weight of Astro 1 on their planet, we use the formula for weight:

\[ W_1 = m_1 \cdot g_1 \]

where \( m_1 = 60 \, \text{kg} \) is the mass of Astro 1 and \( g_1 = 7.0 \, \text{m/s}^2 \) is the gravitational acceleration on Astro 1's planet.

\[ W_1 = 60 \, \text{kg} \times 7.0 \, \text{m/s}^2 = 420 \, \text{N} \]

Astro 2 wants to experience the same weight as Astro 1, which is 420 N. Therefore, we set Astro 2's weight equal to 420 N:

\[ W_2 = m_2 \cdot g_2 = 420 \, \text{N} \]

where \( m_2 = 80 \, \text{kg} \) is the mass of Astro 2 and \( g_2 \) is the gravitational acceleration on Astro 2's planet.

Rearrange the equation to solve for \( g_2 \):

\[ g_2 = \frac{W_2}{m_2} = \frac{420 \, \text{N}}{80 \, \text{kg}} \]

Calculate \( g_2 \):

\[ g_2 = 5.25 \, \text{m/s}^2 \]

Final Answer