A rock is dropped from rest from a height above a strange planet, and a strobe-light photograph is taken. The image is damaged in transmission to earth so that an unknown part of the top of the picture is lost. However, five successive images of the falling rock can be seen. The spacing between the remaining images corresponds to 3.1570 m, 3.2390 m, 3.3210 m, and 3.4030 m, and the flash rate is 10.0 flashes per second. Calculate the acceleration of gravity on that planet ( m/s2).

To calculate the acceleration of gravity on the planet, we can use the equation:

d = (1/2) * g * t^2

where:
d is the distance between the images
g is the acceleration due to gravity
t is the time interval between the flashes

We can start by calculating the time intervals between the flashes:

t1 = 1/10 = 0.1 seconds
t2 = 2 * 0.1 = 0.2 seconds
t3 = 3 * 0.1 = 0.3 seconds
t4 = 4 * 0.1 = 0.4 seconds

Now, we can substitute the values of d and t into the equation to find the acceleration due to gravity:

d1 = (1/2) * g * t1^2
3.1570 = (1/2) * g * (0.1)^2
3.1570 = (1/2) * g * 0.01
31.57 = g * 0.01

d2 = (1/2) * g * t2^2
3.2390 = (1/2) * g * (0.2)^2
3.2390 = (1/2) * g * 0.04
80.975 = g * 0.04

d3 = (1/2) * g * t3^2
3.3210 = (1/2) * g * (0.3)^2
3.3210 = (1/2) * g * 0.09
73.8 = g * 0.09

d4 = (1/2) * g * t4^2
3.4030 = (1/2) * g * (0.4)^2
3.4030 = (1/2) * g * 0.16
42.51875 = g * 0.16

Now, we can solve the system of equations to find g:

31.57 = 0.01g
80.975 = 0.04g
73.8 = 0.09g
42.51875 = 0.16g

Let's divide the second equation by the first equation:

(80.975/0.04) = (0.04g/0.01g)
2024.375 = 4g/1
2024.375 = 4g

Now, divide the third equation by the second equation:

(73.8/0.09) = (0.09g/0.04g)
820 = 2.25g/1
820 = 2.25g

Finally, divide the fourth equation by the third equation:

(42.51875/0.16) = (0.16g/0.09g)
265.1171875 = 1.77777778g/1
265.1171875 = 1.77777778g

Now, we have three equations:

2024.375 = 4g
820 = 2.25g
265.1171875 = 1.77777778g

By solving these equations simultaneously, we can find the value of g.

To calculate the acceleration of gravity on the strange planet, we can use the formula for acceleration due to gravity:

g = 2d / t^2

Where:
g is the acceleration of gravity
d is the distance covered by the falling object
t is the time interval between successive images

First, let's find the time interval between each image using the flash rate of 10.0 flashes per second. Since we have five images, the total time is:

Total time = 5 images / 10 flashes per second = 0.5 seconds

Now, let's calculate the average distances:

Average distance = (3.1570 m + 3.2390 m + 3.3210 m + 3.4030 m) / 4 = 3.28025 m

Next, we'll use the formula to find the acceleration of gravity:

g = 2d / t^2

g = 2 * 3.28025 m / (0.5 s)^2

g = 13.121 m / 0.25 s^2

g = 52.484 m/s^2

Therefore, the acceleration of gravity on the strange planet is approximately 52.484 m/s^2.