Question

The projectile has maximum value of time of flight tjen the angle of projection is 1) 90° 2) 60° 3) 45° 4) 30°

Answer 1

The projectile has maximum value of time of flight when the angle of projection is 90° . Thus , the option (1) is the correct option .

• Time of flight in a projectile is ( 2 * u * Sinθ ) / g .

• Sinθ is maximum at 90° . Value of Sin 90° is 1 .
• Thus ,  at the angle of projection of 90° , the projectile has maximum value of time of flight that is equal to ( 2 * u ) / g .

Answer 2

The correct option is option (1).

Explanation:

Time of Flight:

Time taken by a projectile to complete entire trajectory is called the time of flight of the object.

Let

u be the initial velocity of projection

$\theta$ be angle of projection.

The initial velocity can expressed as x components and y components

$u_x=u cos\theta$

$u_y=u.sin\theta$

The displacement formula :

$y=ut-\frac12 at^2$

$y$ =displacement along vertically

t= time of flight.

To find time of flight, putting y=0 and initial velocity in vertically is $u_y=u.sin\theta$

$\therefore 0=(u.sin\theta) t-\frac12 gt^2$

$\Rightarrow utsin\theta=\frac 12 gt^2$

$\Rightarrow usin\theta=\frac 12 gt$

$\Rightarrow t=\frac{2u sin \theta}{g}$

The maximum value of $sin\theta$ is 1,it means $\theta=90^\circ$

The projectile has maximum value of time fight trajectory the angle of projection is 90°.