The tallest volcano in the solar system is the
29 km tall Martian volcano, Olympus Mons.
An astronaut drops a ball off the rim of the
crater and that the free fall acceleration of the
ball remains constant throughout the ball’s
29 km fall at a value of 4.1 m/s2. (We assume
that the crater is as deep as the volcano is tall,
which is not usually the case in nature.)
Find the time for the ball to reach the crater
floor.
y = yi + vi t + (1/2) a t^2
yi = 29*10^3
y = 0 at bottom
vi = 0
a = - 4.1
so
0 = 29*10^3 - 2.05 t^2
t = 119 seconds = about two minutes
To find the time it takes for the ball to reach the crater floor, we can use the equation of motion for free fall:
s = ut + (1/2)at^2
Where:
s = distance (in this case, the height of the volcano, which is 29 km or 29,000 meters)
u = initial velocity (which is 0 since the ball is dropped, and there is no initial upward velocity)
a = acceleration (which is given as 4.1 m/s^2)
t = time
Since we're looking for the time for the ball to reach the crater floor, which is the height of the volcano, we substitute s = 29,000 m into the equation:
29,000 = 0 + (1/2)(4.1)t^2
Simplifying the equation further:
29,000 = 2.05t^2
Now we can solve for t. Dividing both sides of the equation by 2.05:
t^2 = 29,000 / 2.05
t^2 = 14,146.34
Taking the square root of both sides:
t = √14,146.34
t ≈ 118.9 seconds
Therefore, it will take approximately 118.9 seconds for the ball to reach the crater floor.