If an object is dropped from a height of [tex]$h$[/tex] meters and hits the ground in [tex]$t$[/tex] seconds, then [tex]$t=\sqrt{\frac{h}{4.9}}$[/tex].

Suppose that an object is dropped from the top of a building that is 135.73 meters tall. How long does it take to hit the ground?

Round your answer to the nearest tenth.



Answer :

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.