Question

Define maximum vertical height. Derive an expression for maximum vertical height attained by a body projected at an angle with respect to horizontal.

Answer 1

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11th

Physics

Motion in a Plane

Projectile Motion

Derive an expression for ma...

PHYSICS

Derive an expression for maximum height and range of an object in projectile motion.

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ANSWER

Let a projectile move with a velocity u which is inclined with the horizontal at angle of θ. The velocity after time 't' will be

v=v

x

i

^

+v

y

j

^

v=ucosθ

i

^

+(usinθ−gt)

j

^

(Since:v

y

=usinθ−gt)

At maximum height the projectile will only have horizontal component that is

v

x

=ucosθ

v

y

2

−u

y

2

=2ay

v

y

=0(atmaxheightH)

u

y

=usinθ

ay=−gH

Puttingthesevalues,

0=(usinθ)

2

−2gH

H=

2g

u

2

sin

2

θ

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