**Given:**
- The acceleration due to gravity on planet A is 9 times the acceleration due to gravity on planet B.
- A man jumps to a height of 2 m on the surface of planet A.

**To find:**
The height of the jump by the same person on planet B.

**Solution:**
Let's assume the acceleration due to gravity on planet B is 'g'.

**Step 1: Calculate the acceleration due to gravity on planet A**
Given that the acceleration due to gravity on planet A is 9 times the acceleration due to gravity on planet B, we can write:
Acceleration due to gravity on planet A = 9g

**Step 2: Calculate the time taken to reach maximum height on planet A**
To calculate the time taken to reach the maximum height on planet A, we can use the equation:
v^2 - u^2 = 2as
where,
v = final velocity (0 m/s at the maximum height)
u = initial velocity (unknown)
a = acceleration due to gravity on planet A (9g)
s = displacement (2 m)

Since the final velocity is 0 m/s, the equation becomes:
0 - u^2 = 2(9g)(2)
- u^2 = 36g
u^2 = -36g

Taking the square root of both sides, we get:
u = √(-36g)
u = √(36g) * i
u = 6√g * i

where i is the imaginary unit.

**Step 3: Calculate the time taken to reach maximum height on planet B**
To calculate the time taken to reach the maximum height on planet B, we can use the same equation as in Step 2 with the acceleration due to gravity on planet B (g) and the same displacement (2 m).

0 - u^2 = 2g(2)
- u^2 = 4g
u^2 = -4g

Taking the square root of both sides, we get:
u = √(-4g)
u = √(4g) * i
u = 2√g * i

**Step 4: Calculate the height of the jump on planet B**
To calculate the height of the jump on planet B, we can use the equation:
s = ut + (1/2)at^2
where,
s = displacement (unknown)
u = initial velocity (2√g * i)
a = acceleration due to gravity on planet B (g)
t = time taken to reach maximum height (unknown)

Since the final displacement is 0 m at the maximum height, the equation becomes:
0 = (2√g * i)t + (1/2)g(t^2)
0 = 2√g * it + (1/2)gt^2

Dividing the entire equation by g, we get:
0 = 2√g * it + (1/2)t^2

Since 'i' is the imaginary unit, it can be canceled out. Therefore, the equation becomes:
0 = 2√g * t + (1/2)t^2

Simplifying the equation, we get:
0 = t(2√g + (1/2)t)

Since time cannot be zero, we can ignore the first factor on