A body is projected with a velocity 14 km/s from the surface of the earth. Find the velocity of body at infinity. Escape velocity at the surface of the earth is 11.2 km/s.

Solution

Let v_∞ be the velocity of body at infinity.
By using law of conservation of energy, we have
$space space space space 1 half mv squared minus GMm over straight R equals 1 half mv subscript infinity superscript 2 plus 0$
$rightwards double arrow$ $space space space space 1 half mv squared minus 1 half mv subscript straight e superscript 2 equals 1 half mv subscript infinity superscript 2$

$rightwards double arrow$ $straight v subscript infinity equals square root of straight v squared minus straight v subscript straight e superscript 2 end root$
Here, we have
Velocity with which the body is projected, $straight v equals 14 space km divided by straight s$
Escape velocity, $straight v subscript straight e equals 11.2 space km divided by straight s$
∴ Velocity of body at infinity, $straight v subscript infinity space equals space square root of left parenthesis 14 right parenthesis squared minus left parenthesis 11.2 right parenthesis squared end root space equals space 8.4 space km divided by straight s$

Some More Questions From Motion in Straight Line Chapter

State which of the following are examples of one, two or three dimensional motion:

(a) A kite flying in the sky.

(b) The earth revolving around the sun.

(c) A train moving along the equator of the earth in clockwise direction.

(d) Accelerated motion of a particle in a straight line.

For Daily Free Study Material Join wiredfaculty

Motion In Straight Line

A body is projected with a velocity 14 km/s from the surface of the earth. Find the velocity of body at infinity. Escape velocity at the surface of the earth is 11.2 km/s.

Some More Questions From Motion in Straight Line Chapter

Can you think of physical phenomena involving the moon in which moon cannot be treated as particle?

A train is crossing the bridge. Can it be taken as a particle?

Can a train be taken a particle? Give an example in support of your answer.

A particle is moving along curved line in space. Is the motion one dimensional?

State which of the following are examples of one, two or three dimensional motion:

(a) A kite flying in the sky.

(b) The earth revolving around the sun.

(c) A train moving along the equator of the earth in clockwise direction.

(d) Accelerated motion of a particle in a straight line.

Define distance.

Define displacement.

Can magnitude of displacement be greater than distance travelled by particle?

A body is thrown with a velocity of 9.8 m/s in the vertical upward direction. What is the velocity after one second?

Mock Test Series

NCERT Sample Papers

Entrance Exams Preparation

Phone Number

Email Address

Loaction

For Daily Free Study Material Join wiredfaculty

Motion In Straight Line

A body is projected with a velocity 14 km/s from the surface of the earth. Find the velocity of body at infinity. Escape velocity at the surface of the earth is 11.2 km/s.

Some More Questions From Motion in Straight Line Chapter

Can you think of physical phenomena involving the moon in which moon cannot be treated as particle?

A train is crossing the bridge. Can it be taken as a particle?

Can a train be taken a particle? Give an example in support of your answer.

A particle is moving along curved line in space. Is the motion one dimensional?

State which of the following are examples of one, two or three dimensional motion: (a) A kite flying in the sky. (b) The earth revolving around the sun. (c) A train moving along the equator of the earth in clockwise direction. (d) Accelerated motion of a particle in a straight line.

Define distance.

Define displacement.

Can magnitude of displacement be greater than distance travelled by particle?

A body is thrown with a velocity of 9.8 m/s in the vertical upward direction. What is the velocity after one second?

Mock Test Series

NCERT Sample Papers

Entrance Exams Preparation

State which of the following are examples of one, two or three dimensional motion:

(a) A kite flying in the sky.

(b) The earth revolving around the sun.

(c) A train moving along the equator of the earth in clockwise direction.

(d) Accelerated motion of a particle in a straight line.