The equation of projectile is y = 16 x - 5 x 2 4 . Find the horizontal range.

Given, Equation of projectile, y = 16 x - 5 x 2 4 . Horizontal range is the horizontal displacement of the projectile when its vertical displacement becomes zero, i.e., when y = 0 . On substituting, y = 0 in the given equation of trajectory, 0 = 16 x - 5 x 2 4 x = 64 5 = 12 . 8 unit .

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A particle is projected over a triangle from one extremity of its horizontal base. Grazing over the vertex, it falls on the other extremity of the base. If $a$ and $b$ are the base angles of the triangle and $θ$ the angle of projection, prove that $tanθ =$ $\tan α + \tan β$ .

Important Questions on Kinematics II

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JEE Advanced

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PHYSICS For Joint Entrance Examination JEE (Advanced) Mechanics I>Chapter 5 - Kinematics II>ILLUSTRATION 5.21>Q (a)

A particle projected at a definite angle

α

to the horizontal passes through points

(a, b)

and

(b, a)

, referred to horizontal and vertical axes through the point of projection. Show that:
(a) The horizontal range

R = \frac{a^{2} + a b + b^{2}}{a + b}

(b) The angle of projection

α

is given by

\tan^{- 1} [\frac{a^{2} + a b + b^{2}}{a b}]

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JEE Advanced

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PHYSICS For Joint Entrance Examination JEE (Advanced) Mechanics I>Chapter 5 - Kinematics II>CONCEPT APPLICATION EXERCISE 5.2>Q 1

The equation of projectile is

y = 16 x - \frac{5 x^{2}}{4}

. Find the horizontal range.

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JEE Advanced

IMPORTANT

PHYSICS For Joint Entrance Examination JEE (Advanced) Mechanics I>Chapter 5 - Kinematics II>CONCEPT APPLICATION EXERCISE 5.2>Q 2

A particle is thrown with the velocity

u

at an angle

α

from the horizontal. Another particle is thrown with the same velocity at an angle

α

from the vertical. What will be the ratio of times of flight of two particles?

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JEE Advanced

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PHYSICS For Joint Entrance Examination JEE (Advanced) Mechanics I>Chapter 5 - Kinematics II>CONCEPT APPLICATION EXERCISE 5.2>Q 3

The figure below shows four paths for a kicked football. Ignoring the effects of air on the flight, rank the paths according to the initial horizontal velocity component, the highest first.

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JEE Advanced

IMPORTANT

PHYSICS For Joint Entrance Examination JEE (Advanced) Mechanics I>Chapter 5 - Kinematics II>CONCEPT APPLICATION EXERCISE 5.2>Q 4

A projectile is thrown into space to have maximum horizontal range $R$ . Taking the point of projection as origin, find out the coordinates of the point where the speed of the particle is minimum.

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JEE Advanced

IMPORTANT

PHYSICS For Joint Entrance Examination JEE (Advanced) Mechanics I>Chapter 5 - Kinematics II>CONCEPT APPLICATION EXERCISE 5.2>Q 5

Many bullets are fired in all directions at the same speed

u

. What is the maximum area on the ground on which these bullets will spread?

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JEE Advanced

IMPORTANT

PHYSICS For Joint Entrance Examination JEE (Advanced) Mechanics I>Chapter 5 - Kinematics II>CONCEPT APPLICATION EXERCISE 5.2>Q 6

A projectile is thrown with an initial speed

u

and the angle of projection

15 °

to the horizontal has a range

R

. If the same projectile is thrown at an angle of

45 °

to the horizontal with speed

2 u

, what will be its range?

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JEE Advanced

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PHYSICS For Joint Entrance Examination JEE (Advanced) Mechanics I>Chapter 5 - Kinematics II>CONCEPT APPLICATION EXERCISE 5.2>Q 7

The range

R

of a projectile is the same when its maximum heights are

h_{1}

and

h_{2}

. What is the relation between

R

and

h_{1}

and

h_{2}

A particle is projected over a triangle from one extremity of its horizontal base. Grazing over the vertex, it falls on the other extremity of the base. If a and b are the base angles of the triangle and θ the angle of projection, prove that tanθ=tanα+tanβ.

Important Questions on Kinematics II

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A particle is projected over a triangle from one extremity of its horizontal base. Grazing over the vertex, it falls on the other extremity of the base. If $a$ and $b$ are the base angles of the triangle and $θ$ the angle of projection, prove that $tanθ =$ $\tan α + \tan β$ .