Final answer:
The correct answer is option A. 5(√3−1)
Step-by-step explanation:
To find the minimum time after which the projectile's inclination with the horizontal is 45 degrees, we need to find the time it takes for the projectile to reach its highest point. From there, we can calculate the time it takes for the projectile to reach an inclination of 45 degrees.
We know that the initial speed of the projectile is 100 m/s and the angle with the horizontal is 60 degrees. Using the equations of projectile motion, we can find the time taken to reach the highest point:
t = (2 * initial vertical velocity) / acceleration due to gravity
Once we have the time taken to reach the highest point, we can calculate the total time taken for the inclination to be 45 degrees using:
total time = 2 * time to reach highest point
Plugging in the given values, we find that the minimum time after which the inclination with the horizontal is 45 degrees is 5*(√3−1) seconds (option A).