Question

1. 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
1.4 s
0.39 s
0.07 s
0.14 s

Explanation:

Step1: Identify the vertical - motion parameters

The giraffes fall vertically. The vertical - displacement \(y = 0.70\ m\), the initial vertical velocity \(u_y=0\ m/s\), and the acceleration due to gravity \(g = 9.8\ m/s^{2}\). We use the equation of motion for vertical displacement \(y=u_y t+\frac{1}{2}gt^{2}\).

Step2: Substitute the values into the equation

Since \(u_y = 0\ m/s\), the equation simplifies to \(y=\frac{1}{2}gt^{2}\). We can solve for \(t\), so \(t=\sqrt{\frac{2y}{g}}\).

Step3: Calculate the time

Substitute \(y = 0.70\ m\) and \(g = 9.8\ m/s^{2}\) into the formula: \(t=\sqrt{\frac{2\times0.70}{9.8}}=\sqrt{\frac{1.4}{9.8}}\approx\sqrt{0.143}\approx0.38\ s\).

Answer:

0.38 s