Use the table of data for two falling rocks to answer the question
Rock 1. Rock 2
Mass (kg). 2.5. 25
Height of fall (m). 78.4. 78.4
Time to fall. 4.0. ?
Based on this data, how many seconds will it take rock 2 to fall?
Based on the given data, we can assume that both rocks are falling from the same height (78.4m) and we are trying to find the time it takes for rock 2 to fall to the ground.
To find the time for rock 2 to fall, we can use the formula:
time = sqrt(2 * height / acceleration due to gravity)
Since both rocks are falling under the same gravitational acceleration, we can assume a value of 9.8 m/s^2 for acceleration due to gravity.
For rock 1:
time for rock 1 = sqrt(2 * 78.4 / 9.8) = sqrt(2 * 8) = sqrt(16) = 4.0 seconds
Given that rock 1 and rock 2 have the same height of fall (78.4m) and they are both falling under the same gravitational acceleration, we can conclude that rock 2 will also take 4.0 seconds to fall to the ground.
To determine how many seconds it will take for rock 2 to fall, we can use the concept of time of flight for objects falling freely. The time of flight depends on the height of the fall and the acceleration due to gravity, which is approximately 9.8 m/s² on Earth.
Given that rock 1 and rock 2 have the same height of fall (78.4 m), we can use the formula:
Time = sqrt(2 * height / acceleration)
For rock 1:
Time = sqrt(2 * 78.4 / 9.8) ≈ sqrt(16) ≈ 4.0 seconds
Since the masses of rock 1 and rock 2 are different, it does not affect the time of fall. Therefore, rock 2 will also take approximately 4.0 seconds to fall.
To determine the time it takes for rock 2 to fall, we can use the equation for gravitational potential energy:
Potential Energy (PE) = mass (m) x gravitational constant (g) x height (h)
For both rocks, the height of fall is given as 78.4 meters. The mass of rock 1 is 2.5 kg, and the mass of rock 2 is 25 kg. The gravitational constant, denoted as "g," is approximately 9.8 m/s^2.
Plugging in the values for rock 1:
PE1 = 2.5 kg x 9.8 m/s^2 x 78.4 m
Simplifying this equation, we find that the potential energy of rock 1 is:
PE1 = 1924.8 J
Since the potential energy of both rocks is the same, we can equate the two equations:
PE1 = PE2
1924.8 J = 25 kg x 9.8 m/s^2 x h
Solving for the height (h) of rock 2:
h = 1924.8 J / (25 kg x 9.8 m/s^2)
h ≈ 7.91 m
Now, to find the time (t) it takes for rock 2 to fall from a height of 7.91 meters, we can use the equation for free fall:
h = (1/2) x g x t^2
Plugging in the known values:
7.91 m = (1/2) x 9.8 m/s^2 x t^2
Simplifying this equation:
t^2 = (2 x 7.91 m) / 9.8 m/s^2
t ≈ sqrt((2 x 7.91 m) / 9.8 m/s^2)
t ≈ sqrt(1.6 s^2)
t ≈ 1.26 s
Therefore, it will take approximately 1.26 seconds for rock 2 to fall from a height of 78.4 meters.