Question

A body is projected from the ground with some velocity. Three seconds later the body is moving in a direction making an angle of 30° with the horizontal and two seconds later it moves horizontally. Find the distance at which the body will fall on the ground from the point of projection.

Solution

Let the body be projected with velocity u making an angle θ with the horizontal.
The direction of motion of body after t seconds of throw is given by the equation,
$tan space straight alpha space equals space fraction numerator straight u space sin space straight theta space minus space gt over denominator straight u space cos space straight theta end fraction$
Here at time, t = 3 the value of $straight alpha$ is $30 degree$ and at t = 5s the value of $straight alpha$ is $0 degree.$
∴ $tan space 30 degree space equals space fraction numerator straight u space sinθ minus 30 over denominator straight u space cosθ end fraction$ ...(1)
and
$tan space 0 degree space equals space fraction numerator straight u space sinθ minus 50 over denominator straight u space cosθ end fraction$ ...(2)
From (2),

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Substituting $straight u space sinθ space equals 50$ in equation (1), we get
 $straight u space cos space straight theta space equals space fraction numerator straight u space sinθ minus 30 over denominator tan 30 degree end fraction equals 20 square root of 3$ ...(4)
The horizontal range of the body,
$space space space space straight R equals fraction numerator straight u squared sin 2 straight theta over denominator straight g end fraction equals fraction numerator 2 straight u space sinθ space straight u space cosθ over denominator straight g end fraction$

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Therefore, the body falls at a distance of 200 $square root of 3$ from the point of projection.

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Motion In A Plane

A body is projected from the ground with some velocity. Three seconds later the body is moving in a direction making an angle of 30° with the horizontal and two seconds later it moves horizontally. Find the distance at which the body will fall on the ground from the point of projection.

Some More Questions From Motion in A Plane Chapter

What are the basic characteristics that a quantity must possess so that it may be a vector quantity?

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Name a quantity which is both scalar as well as vector.

Which of the followings is/are vector quantities: work, power, acceleration, mass, momentum?

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For Daily Free Study Material Join wiredfaculty

Motion In A Plane

A body is projected from the ground with some velocity. Three seconds later the body is moving in a direction making an angle of 30° with the horizontal and two seconds later it moves horizontally. Find the distance at which the body will fall on the ground from the point of projection.

Some More Questions From Motion in A Plane Chapter

What are the basic characteristics that a quantity must possess so that it may be a vector quantity?

Is a physical quantity, having a direction, necessarily a vector?

Name a quantity which is both scalar as well as vector.

Which of the followings is/are vector quantities: work, power, acceleration, mass, momentum?

Pick up the odd one from the following: force, linear momentum, mass, impulse.

Pick out the only vector quantities in the following list:Temperature, pressure, impulse, time, power, total path length, energy, gravitational potential, coefficient of friction and charge.

Pick out the two scalar quantities in the following list: force, angular momentum, work, current, linear momentum, electric field, average velocity, magnetic moment, reaction as per Newton’s third law, relative velocity.

What are polar vectors?

Give two examples of polar vectors.

What are axial vectors?

Mock Test Series

NCERT Sample Papers

Entrance Exams Preparation

Pick out the only vector quantities in the following list:
Temperature, pressure, impulse, time, power, total path length, energy, gravitational potential, coefficient of friction and charge.

Pick out the two scalar quantities in the following list:
force, angular momentum, work, current, linear momentum, electric field, average velocity, magnetic moment, reaction as per Newton’s third law, relative velocity.