An astronaut on Triton throws a 0.142 kg baseball straight up with a velocity of 24 m/s. How high does the baseball go?
To find the height that the baseball reaches, you can use the equations of motion and the principles of physics. Here's the step-by-step process to solve this problem:
1. Identify the relevant equations: To determine the height, we can use the equation for height in freefall, which is given as:
h = (v^2 - u^2) / (2 * g)
Where:
h = height
v = final velocity
u = initial velocity
g = acceleration due to gravity
2. Determine the values: Given in the problem are:
mass of the baseball (m) = 0.142 kg
initial velocity of the baseball (u) = 24 m/s
Now, we need to find the acceleration due to gravity on Triton (g). The acceleration due to gravity on Triton is approximately 1.38 m/s^2, which is about 1/10th of the acceleration due to gravity on Earth.
3. Plug the values into the equation: Substituting the values into the equation, we get:
h = (24^2 - 0) / (2 * 1.38)
4. Calculate the height: Now, performing the calculations, we find:
h = (576 - 0) / 2.76
h = 576 / 2.76
h ≈ 208.70 meters
Therefore, the baseball reaches a height of approximately 208.70 meters on Triton.