Question

a missile is fired with velocity 30 metre per second making an angle 60° with the horizontal after reaching maximum height its velocity would be​

Answer 1

Answer:

Given:

Missile fired with velocity = 30 m/s

Angle of Projection = 60°

To find:

Velocity after it reaches the max height

Concept:

A Projectile motion can be imagined as simultaneously occuring 2 linear motion (one in the X axis and another in Y axis).

Now , acceleration due to gravity changes only the y component of velocity . As a result of this, the x axis component remains constant.

At the max height, the y axis component of Velocity becomes zero, By the Projectile still has the x -axis velocity.

Hence the velocity at highest point will be :

$\boxed{\red{\large{\bold{ \sf{v( highest \: point)} = \: u \cos( \theta)}}}}$

$\sf{v( highest \: point)} = \: 30 \cos( 60\degree)$

$\sf{v( highest \: point)} = \: 30 \times \dfrac{1}{2}$

$\sf{v( highest \: point)} = 15 \:m{s}^{-1}$

So final answer :

$\boxed{\blue{\large{\bold{\sf{v( highest \: point)} = 15 \:m{s}^{-1}}}}}$

Answer 2

SoLuTioN :

➡ Given:

✏ Initial velocity of missile = 30 m/s

✏ Angle of projection = 60°

➡ To Find:

✏ Velocity of missile at maximum height ??

➡ Concept:

✏ Perpendicular components of initial velocity in projectile motion is given by

$\star\sf \: \red{u{ \tiny{x}} = ucos \theta} \\ \\ \star \sf \: \blue{ u{ \tiny{y}} = usin \theta}$

✏ $\theta$ = angle of projection

✏ u = initial velocity

➡ Formula:

✏ Velocity at any point in projectile motion is given by

$\star \sf \: \green{v{ \tiny{p}} = \sqrt{ {v{ \tiny{x}}}^{2} + {v{ \tiny{y}}}^{2} } }$

✏ As we know that...

$\star \sf \: \underline{v{ \tiny{x}} = ucos \theta} \: and \: \underline{v{ \tiny{y}} = usin \theta - gt}$

➡ Calculation:

✏ At maximum height Vy = 0

$\implies \sf \: v{ \tiny{p}} = \sqrt{ {(ucos \theta)}^{2} } \\ \\ \implies \sf \: v{ \tiny{p}} = \sqrt{ {(30cos60 \degree)}^{2} } \\ \\ \implies \sf \: v{ \tiny{p}} = \sqrt{ \frac{900}{4} } = \sqrt{225} \\ \\ \orange{ \bigstar} \: \underline{ \boxed{ \bold{ \sf{v{ \tiny{p}} = 15 \: \frac{m}{s}}}}} \: \orange{ \bigstar}$