Question

A player P kicks the football with velocity 20 m/s at angle of 15°. Another player Q on the goal line 12 m away in the direction of kick, runs at the same instant to meet the ball. With what speed he should run so that he could catch the ball just before it hits the ground? (Take g = 10 m/s²).

Solution

We know that,
Horizontal range, $straight R equals fraction numerator straight u squared sin 2 straight theta over denominator straight g end fraction$
We have,
$Initial space velocity comma space straight u equals 20 straight m divided by straight s Angle space of space projecvtion comma space straight theta equals 15 degree a c c e l e r a t i o n space d u e space t o space g r a v i t y comma space straight g equals 10 space straight m divided by straight s squared$
∴
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i.e. the ball hits the ground at a distance of 20m from the position of player P.
Since the player Q is 12m away, therefore, he has to travel a distance 8m to catch the ball in time equal to the time of flight.
Now the time of flight is,
$space space space space straight T equals fraction numerator 2 straight u space s i n theta over denominator straight g end fraction space space space space space space equals fraction numerator 2 cross times 20 cross times s i n 15 degree over denominator 10 end fraction space space space space space space space equals 4 s i n 15 degree$
$rightwards double arrow$ $straight T equals 1.035 space straight s$
The velocity of player Q is,
$straight v equals fraction numerator 8 over denominator 1.035 end fraction equals 7.727 space straight m divided by straight s$

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Motion In A Plane

A player P kicks the football with velocity 20 m/s at angle of 15°. Another player Q on the goal line 12 m away in the direction of kick, runs at the same instant to meet the ball. With what speed he should run so that he could catch the ball just before it hits the ground? (Take g = 10 m/s²).

Some More Questions From Motion in A Plane Chapter

What is a vector quantity?

Give three examples of scalar quantities.

Give three examples of vector quantities.

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.

Mock Test Series

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Entrance Exams Preparation

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Motion In A Plane

A player P kicks the football with velocity 20 m/s at angle of 15°. Another player Q on the goal line 12 m away in the direction of kick, runs at the same instant to meet the ball. With what speed he should run so that he could catch the ball just before it hits the ground? (Take g = 10 m/s2).

Some More Questions From Motion in A Plane Chapter

What is a vector quantity?

Give three examples of scalar quantities.

Give three examples of vector quantities.

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.

Mock Test Series

NCERT Sample Papers

Entrance Exams Preparation

A player P kicks the football with velocity 20 m/s at angle of 15°. Another player Q on the goal line 12 m away in the direction of kick, runs at the same instant to meet the ball. With what speed he should run so that he could catch the ball just before it hits the ground? (Take g = 10 m/s²).

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.