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? 0.38 s 0.07 s 1.4 s 0.14 s

Explanation:

Step1: Identify the vertical - motion problem

The giraffes are in free - fall in the vertical direction. The vertical displacement $y = 0.70$m, and the initial vertical velocity $u_y=0$m/s. The equation for vertical displacement in free - fall is $y = u_y t+\frac{1}{2}gt^{2}$. Since $u_y = 0$m/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, $t=\sqrt{\frac{2y}{g}}$. Given $y = 0.70$m and $g = 9.8$m/s², we substitute these values 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