Question

An astronaut is stranded on a distant planet. He needs to send a message rocket home so he can be rescued. In order to launch the rocket successfully, the astronaut must know the acceleration of gravity on this planet. He takes the following data by dropping a rock from the top of a tree:

Time (s)	Position Trial 1 (m)	Position Trial 1 (m)	Position Trial 1 (m)	Average Position (m)
1.0	4.153	4.21	4.162
2.0	16.05	17.11	16.94
3.0	38.02	37.505	37.20
4.0	65.98	66.24	68.18

Calculate the average position of the rock. Assume the initial velocity of the rock is zero. On a separate sheet of graph paper, plot the average position versus the square of the time to find the acceleration due to gravity. Write the value below:

Answer 1

Data table: Time (s) Position aiPosition tail2 Position tail3Average 1.0 2.0 3.0 4.0 4.153 16.05 38.02 65.98 4.162 16.94 37.20 68.18 osition (m 4.175 16.7 37.575 66.8 4.21 37.505 66.24 Table: average position and corresponding square of the time. Time Sqaure of the time Average position (m) 4.175 16.7 37.575 66.8 2 4 9 16 4

The graph average position verses square of the time: 80 70 y4.175x 60 8 50 40 E 30 20 10 10 12 14 16 18 2 4 Sqaure of the time Compare the line equationy-4.175x with the kinematic equation of motion 2 a= 4.175 Therefore, the acceleration due to gravity of the planet is 4.175 m/s