Question

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 1.53 s 2.47 s 6.12 s

Explanation:

Step1: Identify the kinematic - equation

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

Step2: Rearrange the equation for time

From $h=\frac{1}{2}gt^2$, we can solve for $t$. First, multiply both sides by 2 to get $2h=gt^2$. Then, $t=\sqrt{\frac{2h}{g}}$.

Step3: Substitute the values

Given $h = 30\ m$ and $g = 9.8\ m/s^2$, we substitute these values into the formula: $t=\sqrt{\frac{2\times30}{9.8}}=\sqrt{\frac{60}{9.8}}\approx\sqrt{6.12}\approx 2.47\ s$.

Answer:

2.47 s