Question: When an object is dropped, the number of feet N that it falls is given by the formula:\(N=\frac{1}{2}gt^2\), where t is the time in seconds since it was dropped and g is 32.2. If it takes 5 seconds for the object to reach the ground, how many feet does it fall during the last 2 seconds?

1. 64.4
2. 96.6
3. 161.0
4. 257.6
5. 402.5

Answer:
Solution with Explanation:
Approach Solution (1):

The formula is given when the object is dropped from rest. So the distance it covers in the last two seconds will be the distance covered from start till 5 seconds – distance covered from start to 5-2 = 3 seconds

This step is essential as the object already has non-zero velocity when it is 2 seconds before it reaches the ground

Let the distance covered in the last two seconds be d.

\(d = 0.5gt ^ 2 - 0.5gt ^ {'2}\)
\(d=0.5g(t^2-t^{'2})\)

Where t = 5 seconds and t’ = 3 seconds
Hence

d=0.5*32.2*(25-9)
d=16.1*16
d > 256

Only slightly greater

Correct Option: D

Approach Solution (2):

N feet in last 2 seconds can be found here.
If we subtract N in last 5 seconds – N in last 3 seconds

\(N=\frac{1}{2}*32.2[16]\)
N = 257.6

Correct Option: D

Approach Solution (3):

Distance traveled in last 2 seconds = Distance traveled in 5 seconds – Distance traveled in 3 seconds
Distance traveled in 5 seconds = \(\frac{1}{2}*g*t^2=\frac{1}{2}*32.2*5^2=16.1*25\)
Distance traveled in 3 seconds =\(\frac{1}{2}*g*t^2=\frac{1}{2}*32.2*3^2=16.1*9\)
Distance traveled in 2 seconds =16.1*25-16.1*9 = 16.1*16 = 257.6

Correct Option: D

“When an object is dropped, the number of feet N that it falls is given by the formula: \(N=\frac{1}{2}gt^2\), where t is the time in seconds since it was dropped and g is 32.2. If it takes 5 seconds for the object to reach the ground, how many feet does it fall during the last 2 seconds?”- is a topic of the GMAT Quantitative reasoning section of GMAT. This question has been taken from the book “GMAT Official Guide Quantitative Review”. To solve GMAT Problem Solving questions a student must have knowledge about a good amount of qualitative skills. The GMAT Quant topic in the problem-solving part requires calculative mathematical problems that should be solved with proper mathematical knowledge.

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