Question

An athlete can jump a distance of 8.0 m in the broad jump. What is the maximum distance the athlete can jump on the Moon, where the gravitational acceleration is one–sixth that of Earth?

Answer 1

Answer:

1.33 m

Explanation:

Given:

Height jumped by athlete on Earth (y₁) = 8.0 m

Gravitational acceleration on moon is one-sixth of Earth.

So, $g_m=\dfrac{g_E}{6}$

Height jumped by athlete on moon (y₂) = ?  

We know that, from equation of motion, displacement is directly proportional to the gravitational acceleration keeping the remaining quantities constant.

So, $y\propto g$

Setting up a proportion for Earth and moon, we get:

$\dfrac{y_1}{g_E}=\dfrac{y_2}{g_m}\\\\\\y_2=\dfrac{y_1}{g_E}\times g_m$

Now, substitute $g_m=\dfrac{g_E}{6}$. This gives,

$y_2=\dfrac{8.0}{g_E}\times \dfrac{g_E}{6}\\\\\\y_2=\dfrac{8.0}{6}=1.33\ m$

Therefore, the height jumped on moon is 1.33 m.