A projectile is fired with velocity v at angle thita. Find the time when velocity of projectile will make angle 90' with initial direction of velocity?

To find the time when the velocity of the projectile makes an angle of 90 degrees with the initial direction of velocity, we can analyze the vertical component of the projectile's velocity.

Let's break down the velocity into its horizontal and vertical components:

Initial horizontal component of velocity, Vx = v * cos(theta)
Initial vertical component of velocity, Vy = v * sin(theta)

As time progresses, only the vertical component of the velocity changes due to the effect of gravity. The horizontal component remains constant.

The vertical component of velocity can be expressed as a function of time as follows:
Vy(t) = Vy - g * t

Now, let's find the time when the velocity makes an angle of 90 degrees with the initial direction. At this point, the vertical component of the velocity will become zero.

Vy(t) = 0
Vy - g * t = 0

Solving for t:
t = Vy / g

To substitute for Vy, we can use the initial vertical component of velocity:
t = (v * sin(theta)) / g

Thus, the time when the velocity makes an angle of 90 degrees with the initial direction of velocity is given by:
t = (v * sin(theta)) / g