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 4.4 m/s
2. (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.
Answer in units of s.
I have 0=29x10^3-2.2t^2
So t=170.287404, however that isn't right
29,000 / 2.2 = 13182
sqrt of that is 114.8
To find the time it takes for the ball to reach the crater floor, we can use the kinematic equation for free fall motion:
h = ut + (1/2)at^2
Where:
h = height (29 km = 29,000 m)
u = initial velocity (0 m/s, since the ball is dropped)
t = time
a = acceleration due to gravity (4.4 m/s^2)
Plugging in the values:
29,000 = 0t + (1/2)(4.4)(t^2)
Simplifying the equation:
29,000 = 2.2t^2
Dividing both sides of the equation by 2.2:
t^2 = 29,000 / 2.2
Taking the square root of both sides:
t = √(29,000 / 2.2)
Calculating the value:
t ≈ 66.182 s
Therefore, the time it takes for the ball to reach the crater floor is approximately 66.182 seconds.