On the Pluto, the acceleration due to gravity is about -0.42 meters $/ \sec ^{\wedge} 2$.
What is the equation for the height (position) above the surface of the Pluto for an object that is dropped from 125 meters?
How long would it take the object to reach the surface of Pluto?
seconds
On Earth, the equation for the position of the object would be $h=-4.9 t^{2}+125$.
How long does it take the object to reach the ground on Earth?
seconds
Does it take more time to reach the ground on Pluto or Earth?
Pluto
Earth

Step 1 ：The general equation for the height of an object under constant acceleration is given by \(h = h_0 + v_0t + 0.5at^2\), where \(h_0\) is the initial height, \(v_0\) is the initial velocity, \(a\) is the acceleration, and \(t\) is the time. In this case, the object is dropped, so the initial velocity is 0. The initial height is 125 meters, and the acceleration is -0.42 m/s^2. Substituting these values into the equation gives \(h = 125 + 0.5(-0.42)t^2\).

Step 2 ：The equation for the height of the object above the surface of Pluto as a function of time is \(h = 125 - 0.21t^2\). This equation tells us how the height of the object changes over time.

Step 3 ：To find out how long it would take for the object to reach the surface of Pluto, we need to set the height equal to zero and solve for time.

Step 4 ：The solutions to the equation are -24.4 and 24.4. However, time cannot be negative, so we discard the negative solution.

Step 5 ：Therefore, it would take approximately 24.4 seconds for the object to reach the surface of Pluto.

Step 6 ：The final answer is: The time it would take for the object to reach the surface of Pluto is approximately \(\boxed{24.4}\) seconds.