Question

Problem 1.17. The acceleration due to gravity on the planet Ais 8 times the acceleration due to gravity on planet B. A man jumps to a height of 1.5 m on the surface of A. What is the height of jump by the same person on the planet B?​

Answer 1

Answer:

Height of 12 m

Explanation:

Let x the speed of man , while taking jump height be h .

From third equation of motion we have

$\displaystyle{v^2=u^2+2as}$

Here we have v = 0 a = - g

$\displaystyle{0^2=u^2+2\times-g\times h}\\\\\displaystyle{h=\dfrac{u^2}{2g}}$

Now if we considered h_A and h_B height of jump on the planets then

$\displaystyle{\dfrac{h_B}{h_A}=\dfrac{u^2}{2g_B}\times\dfrac{2g_A}{u^2}}\\\\\\\displaystyle{\dfrac{h_B}{h_A}=\dfrac{2g_A}{2g_B}}\\\\\\\displaystyle{\dfrac{h_B}{h_A}=\dfrac{g_A}{g_B} \ [Given \ other \ is \ 8 \ times]}\\\\\\\displaystyle{\dfrac{h_B}{h_A}=\dfrac{8g_B}{g_B}}\\\\\\\displaystyle{h_B=8\times1.5 \ m \ [Given \ height \ 1.5 \ m]}\\\\\displaystyle{h_B=12 \ m}$

Thus height of 12 m  jump by the same person on the planet B .