Sure! Let's solve this step-by-step.
We are given:
- The height [tex]\( h \)[/tex] from which the egg is dropped: [tex]\( h = 155 \)[/tex] meters
- The acceleration due to gravity [tex]\( g \)[/tex]: [tex]\( g = 9.81 \)[/tex] meters per second squared
We need to find the time [tex]\( t \)[/tex] taken for the egg to reach the ground.
In physics, we can use the equation of motion for objects in free fall which is:
[tex]\[ h = \frac{1}{2} g t^2 \][/tex]
Here, [tex]\( h \)[/tex] is the height, [tex]\( g \)[/tex] is the acceleration due to gravity, and [tex]\( t \)[/tex] is the time the object takes to fall.
First, we rearrange this equation to solve for [tex]\( t \)[/tex]:
[tex]\[ t^2 = \frac{2h}{g} \][/tex]
Now, substitute the given values into the equation:
[tex]\[ t^2 = \frac{2 \times 155}{9.81} \][/tex]
Next, evaluate the fraction:
[tex]\[ \frac{2 \times 155}{9.81} \approx 31.60550724 \][/tex]
Finally, take the square root of that result to solve for [tex]\( t \)[/tex]:
[tex]\[ t \approx \sqrt{31.60550724} \approx 5.62142399639066 \][/tex]
Therefore, the time taken for the egg to reach the ground is:
[tex]\[ t \approx 5.62 \text{ seconds} \][/tex]
Thus,
[tex]\[ t \approx 5.62 \text{ s} \][/tex]
