Question

From the tower of height H, a particle is thrown vertically upwards with a speed u. The time taken by the particle to hit the ground is n times that taken by it to reach the highest point of its path. The relation between H,u and n is

2gH = n²u²

gH = (n-2)²u²

2gH = nu²(n-2)²u²

gH = (n-2)²u²

Solution

2gH = nu²(n-2)²u²

Time is taken to reach the maximum height t1 = u/g
If t₂ is the time taken to hit the ground,
i.e, $negative straight H space equals space ut subscript 2 minus 1 half gt subscript 2 superscript 2 straight t subscript 2 space equals space nt subscript 1 minus straight H space equals space straight u nu over straight g minus 1 half straight g fraction numerator straight n squared straight u squared over denominator straight g squared end fraction minus straight H space equals space nu squared over straight g minus 1 half fraction numerator straight n squared straight u squared over denominator straight g end fraction 2 gH space equals nu squared left parenthesis straight n minus 2 right parenthesis$

Some More Questions From Motion in Straight Line Chapter

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.

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Motion In Straight Line

Some More Questions From Motion in Straight Line Chapter

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?

How does the displacement of a particle change, when reference point for the position is shifted?

A particle moves from A to B along three different paths. Is the displacement along three paths different?

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Motion In Straight Line

From the tower of height H, a particle is thrown vertically upwards with a speed u. The time taken by the particle to hit the ground is n times that taken by it to reach the highest point of its path. The relation between H,u and n is 2gH = n2u2 gH = (n-2)2u2 2gH = nu2(n-2)2u2 gH = (n-2)2u2

Some More Questions From Motion in Straight Line Chapter

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?

How does the displacement of a particle change, when reference point for the position is shifted?

A particle moves from A to B along three different paths. Is the displacement along three paths different?

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.