Question 8 of 10, Step 1 of 1
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The distance that a free falling object falls is directly proportional to the square of the time it falls (before it hits the ground) if an object fell $73 \mathrm{ft}$ in 3 seconds, how far will it have fallen by the end of 4 seconds? Round your answer to the nearest integer if necessary
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Step 1 ：Given that the distance an object falls is directly proportional to the square of the time it falls, we can set up a proportion to solve for the unknown distance. Let's denote the time it takes for the object to fall in the first scenario as 'time1' and the distance it falls as 'distance1'. Similarly, in the second scenario, we'll denote the time as 'time2' and the unknown distance as 'distance2'.

Step 2 ：From the problem, we know that 'time1' is 3 seconds and 'distance1' is 73 feet. We're asked to find 'distance2', the distance the object will have fallen by the end of 'time2', which is 4 seconds.

Step 3 ：Since the distance an object falls is directly proportional to the square of the time it falls, we can say that \(\frac{{distance1}}{{time1^2}} = \frac{{distance2}}{{time2^2}}\). Substituting the given values into this equation, we get \(\frac{{73}}{{3^2}} = \frac{{distance2}}{{4^2}}\).

Step 4 ：Solving this equation for 'distance2', we find that 'distance2' is approximately 130 feet.

Step 5 ：Final Answer: The object will have fallen \(\boxed{130}\) feet by the end of 4 seconds.