Conversations with astronauts on the lunar surface were characterized by a kind of echo in which the earthbound person’s voice was so loud in the astronaut’s space helmet that it was picked up by the astronaut’s microphone and transmitted back to earth. it is reasonable to assume that the echo time equals the time necessary for the radio wave to travel from the earth to the moon and back (that is, neglecting any time delays in the electronic equipment). calculate the distance from earth to the moon given that the echo time was 2.56 s and that radio waves travel at the speed of light (3.00×108 m/s). give your answer in thousands of km.

768000km

Explanation:

Velocity is given by the relation between the distance and the time it takes to travel that distance :

  (1)

In this problem we are told the time it takes for radio wave to travel from the Earth to the Moon and back is the "echo":

 (2)

In addition, we know radio waves are electromagnetic waves (light), and its velocity is:

  (3)

Substituting (2) and (3) in (1):

  (4)

And finding :

  (5)

Finally we can obtain the distance:

massxgravity x heght=weightxheight= pe

4900=490xh

h=10

initial speed when it is dropped is 150 ft/s

now at the same moment the acceleration due to gravity is perpendicular to its velocity

so as we know that

now we have centripetal acceleration a = 32 ft/s^2 as its perpendicular to velocity

while tangential acceleration at the same moment will be zero

so

now radius of curvature is given as

so the radius of curvature just after it is dropped is 703.125 ft