In: Physics
An astronaut on a rock trying to land on a planet his ship was damaged. Although the astronaut does not know the gravitational acceleration
It has a good field of view to measure and measures the height of the rock
takes two measurements to measure. In the first measurement, taking a piece of boulder,
released from the edge of the rock to the ground in 4 s.
measures the fall. In the second, up another rock from the same point
throws correctly. That the piece of rock rose 4 m before it fell to the ground
observes and measures the time to fall to the ground for a total of 8 s. Gravity of the planet
Find the height of the float by finding the acceleration
Case1
Let ‘h’ be the height of fall .
Time ‘t’ = 4 s
For a freefall initial velocity = 0
Let a be the acceleration due to gravity
Using s = ut + 1/2 at2
h = 0 + ½ x a x 42 = 8a
Case 2
Considering the rock is thrown upward from the same position
Splitting this journey in two phases, one upward and another downward
Upward Motion
Height to which the rock reached before fall = 4m
Let u be the initial velocity and v the final velocity
v=0
Let t1 be the time of ascent
Using v2 = u2 + 2as
0 = u2 -2 x a x 4 = u2 - 8a
u2 = 8a
u =
Now using v = u + at1
0 = -at1
at1 =
t1 = / a
Considering the second phase
u=0
t2 = 8- t1 = 8- ( / a ) = ( 8a - ) / a
t22 = ( 8a - )2/a2
Using s = ut + ½ x a x t22
h + 4 = 0 + ½ x a x ( 8a - )2/a2
2a(h+4) = ( 8a - )2
But h= 8a
2a(8a +4 ) = ( 8a - )2
16a2 +8a = 64 a2 +8a – 16a
48a2 = 16a
3a =
9a2 = 8a
a = 8/9 =0.8888 m/s2
h =8a = 8 x 0.8888 = 7.11 m
Height of float = 7.11 m
Acceleration due to gravity = 0.8888 m/s2