Question

lucy and her friend are working at an assembly - plant making wooden toy giraffes. at the end of the line, the giraffes go horizontally off the edge of a conveyor belt and fall into a box below. if the box is 0.70 m below the level of the conveyor belt and 0.50 m away from it, how long does it take for the giraffes to reach the ground? clear all 0.07 s 0.14 s 0.38 s 1.4 s

Explanation:

Step1: Identify the vertical - motion problem

The giraffes fall vertically. The vertical displacement \(y = 0.70m\), and the initial vertical velocity \(u_y=0m/s\). The equation for vertical displacement in free - fall is \(y = u_y t+\frac{1}{2}gt^{2}\), where \(g = 9.8m/s^{2}\). Since \(u_y = 0m/s\), the equation simplifies to \(y=\frac{1}{2}gt^{2}\).

Step2: Solve for time \(t\)

We can re - arrange the equation \(y=\frac{1}{2}gt^{2}\) to solve for \(t\). First, multiply both sides by 2 to get \(2y = gt^{2}\). Then, \(t=\sqrt{\frac{2y}{g}}\). Substitute \(y = 0.70m\) and \(g = 9.8m/s^{2}\) into the formula: \(t=\sqrt{\frac{2\times0.70}{9.8}}=\sqrt{\frac{1.4}{9.8}}\approx\sqrt{0.143}\approx0.38s\).

Answer:

0.38 s