To determine the time it takes for an object to hit the ground when dropped from a height of [tex]\( h \)[/tex] meters, we can use the given formula:
[tex]\[ t = \sqrt{\frac{h}{4.9}} \][/tex]
In this case, the height [tex]\( h \)[/tex] is given as 135.73 meters. We'll follow these steps to find the time [tex]\( t \)[/tex]:
1. Substitute the given height into the formula:
[tex]\[ t = \sqrt{\frac{135.73}{4.9}} \][/tex]
2. Perform the division inside the square root:
[tex]\[ \frac{135.73}{4.9} \approx 27.700 \][/tex]
3. Now, take the square root of the result:
[tex]\[ t = \sqrt{27.700} \][/tex]
4. Calculating the square root gives us the raw time value:
[tex]\[ t \approx 5.263 \][/tex]
5. Round this value to the nearest tenth:
[tex]\[ t \approx 5.3 \][/tex]
Thus, the object takes approximately [tex]\( 5.3 \)[/tex] seconds to hit the ground when dropped from a height of 135.73 meters.
