Question

the table shows the mass of and acceleration due to gravity for several planets in the solar system. if air resistance is ignored, on which planet would a space probe with a mass of 250 kg have the highest speed after falling 25 m?

a. saturn
b. uranus
c. venus
d. earth

Explanation:

Step1: Recall the kinematic equation

The kinematic equation \(v^{2}=v_{0}^{2}+2ah\). Since the probe is dropped (\(v_{0} = 0\)), the equation simplifies to \(v=\sqrt{2ah}\). Here, \(h = 25m\) (constant for all planets).

Step2: Analyze the relationship between \(v\) and \(a\)

From \(v=\sqrt{2ah}\), when \(h\) is constant (\(h = 25m\)), \(v\) is directly proportional to \(\sqrt{a}\) (because \(v=\sqrt{2\times25\times a}=\sqrt{50a}\)). So, the larger the value of \(a\) (acceleration due to gravity), the larger the value of \(v\).

Step3: Compare the values of \(a\) for each planet

For Venus, \(a = 8.9m/s^{2}\); for Earth, \(a=9.8m/s^{2}\); for Uranus, \(a = 8.7m/s^{2}\); for Saturn, \(a=9m/s^{2}\). Since \(9.8>9 > 8.9>8.7\).

Answer:

D. Earth