Question

1. the objects k and l are thrown vertically upwards with initial speeds of vk and vl, as shown in the figure. what is the ratio \\( \frac { v _ { k } } { v _ { l } } \\) if the maximum heights of objects k and l are 2h and h, respectively? (take \\( g = 10 \mathrm { m } / \mathrm { s } ^ { 2 } \\) )

Explanation:

Step1: Use the formula for maximum height

The formula for maximum height \( H=\frac{v^{2}}{2g} \). For object \( K \), \( 2h=\frac{v_{K}^{2}}{2g} \), so \( v_{K}^{2} = 4gh \). For object \( L \), \( h=\frac{v_{L}^{2}}{2g} \), so \( v_{L}^{2}=2gh \).

Step2: Find the ratio of velocities

We want to find \( \frac{v_{K}}{v_{L}} \). From \( v_{K}^{2} = 4gh \) and \( v_{L}^{2}=2gh \), we can write \( \frac{v_{K}^{2}}{v_{L}^{2}}=\frac{4gh}{2gh} = 2 \). Then \( \frac{v_{K}}{v_{L}}=\sqrt{2} \).

Answer:

\(\sqrt{2}\)