By what velocity a ball be projected vertically upwards so that the distance covered in 5th second is twice of that covered in 6th second. (g = 10 m/s2)

To solve this problem, we need to use the equations of motion.

The distance covered in nth second, Sn can be given by the equation:

Sn = u - (1/2)g(n-1)

where: u = initial velocity g = acceleration due to gravity n = nth second

Given in the problem, the distance covered in the 5th second is twice that of the 6th second. So we can write the equation as:

S5 = 2S6

Substituting the values in the equation we get:

u - (1/2)g(5-1) = 2[u - (1/2)g(6-1)]

Solving the above equation, we get:

u - 20 = 2u - 50

Solving for u, we get:

u = 30 m/s

So, the ball should be projected upwards with a velocity of 30 m/s.