Correct Answer - Option 4 : 33 m

The correct answer is option 4) i.e. 33 m

__CONCEPT__:

Kinematic equations of motion:

- These equations define the relationship between initial velocity u, final velocity v, time t, and displacement s of an object with respect to its motion in
**uniform acceleration a**.
- Following are the three
**kinematic equations **for uniformly accelerated motion:

⇒ v = u + at

⇒ s = ut + 0.5at2

⇒ v2 - u2 = 2as

__CALCULATION__:

Given that:

g_{A} =11g_{B} ----(1)

Height of jump on planet A, h_{A} = 3 m

Height of jump on planet b = h_{B}

Using the equation of kinematics, v^{2} - u^{2} = 2gh

When the man jumps, his final velocity v = 0, and the acceleration due to gravity is negative.

⇒ - u2 = 2(-g)h

\(⇒ g = \frac{u^2}{2h}\)

Therefore, \(g_A = \frac{u^2}{2h_A}\) and \(g_B = \frac{u^2}{2h_B}\) ----(2)

From (1) and (2),

\(\Rightarrow \frac{u^2}{2h_A} = 11\frac{u^2}{2h_B}\)

\(\Rightarrow h_B = 11h_A = 11 \times 3 = 33\: m\)

The **height of the jump by the same person on planet B is 33 m.**