Question

1. a 150 - kg pallet initially at rest, falls from a height of 30 m. first, consider the situation ignoring air resistance. calculate how long it will take the pallet to hit the ground. clear all 1.24 s 2.47 s 1.53 s 6.12 s

Explanation:

Step1: Identify the kinematic - equation

The kinematic equation for free - fall motion is $h = v_0t+\frac{1}{2}gt^2$. Since the pallet is initially at rest, $v_0 = 0$. So the equation simplifies to $h=\frac{1}{2}gt^2$, where $h$ is the height, $g$ is the acceleration due to gravity ($g = 9.8\ m/s^2$), and $t$ is the time.

Step2: Solve for time $t$

From $h=\frac{1}{2}gt^2$, we can re - arrange it to get $t=\sqrt{\frac{2h}{g}}$. Given $h = 30\ m$ and $g = 9.8\ m/s^2$, then $t=\sqrt{\frac{2\times30}{9.8}}=\sqrt{\frac{60}{9.8}}\approx\sqrt{6.12}\approx 2.47\ s$.

Answer:

2.47 s