Question

In: Physics

An astronaut on a rock trying to land on a planet his ship was damaged.

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

Solutions

Expert Solution

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


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