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:
gA =11gB ----(1)
Height of jump on planet A, hA = 3 m
Height of jump on planet b = hB
Using the equation of kinematics, v2 - u2 = 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.