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Motion In A Plane

Question
CBSEENPH11018590
Wired Faculty App

Two bodies are placed at a distance 4 km and 6·5 km from the gun. When the bullet is fired at an angle of 30° with horizontal, it hits the body at 4 km. At what angle the bullet should be fired so that it may hit the second body?

Solution

Horizontal range is given by, 
                       straight R equals fraction numerator straight u squared sin space 2 straight theta over denominator straight g end fraction
Therefore the ratio of horizontal ranges R1 and R2 for angles of projections θ1 and θ2 is,
                 space space straight R subscript 1 over straight R subscript 2 equals fraction numerator sin space 2 straight theta subscript 1 over denominator sin space 2 straight theta subscript 2 end fraction
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We have here,
Angle space of space projection comma space straight theta subscript 1 equals 30 degree Horizontal space range comma space straight R subscript 1 space equals space 4 space km Horizontal space range comma space straight R subscript 2 equals 6.5 space km
Therefore, 
sin 2 straight theta subscript 2 equals sin 60 degree cross times fraction numerator 6.5 over denominator 4 end fraction equals 1.407 greater than 1, which is not possible.
Therefore for same speed of bullet, the bullet can not hit the body at a distance of 6·5km.

Some More Questions From Motion in A Plane Chapter

What is a scalar quantity?

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.

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