
Actually Welcome to the Concept of the Projectile Motion.
Since, here given that, vertical velocity= 50m/s
we know that u*sin(theta) = vertical velocity
so the time taken to reach the maximum height or the time of Ascent is equal to
T = Usin(theta) ÷ g, here g = 9.8 m/s^2
so we get as,
T = 50/9.8
T = 5.10 seconds
thus the time taken to reach max height is 5.10 seconds.
For the velocity graph: start at 0s and 4m/s and draw a straight line to 2s and 2 m/s. Then draw a straight horizontal line to 4s and 2m/s
For the acceleration graph: start with a horizontal line from 0s and 2m/s/s to 2s and 2m/s/s. The draw another line from 2 s and 0m/s/s to 4 s and 0m/s/s
Answer:


Explanation:
Here mass density of rod is varying so we have to use the concept of integration to find mass and location of center of mass.
At any distance x from point A mass density


Lets take element mass at distance x
dm =λ dx
mass moment of inertia

So total moment of inertia

By putting the values

By integrating above we can find that

Now to find location of center mass


Now by integrating the above


So mass moment of inertia
and location of center of mass 