Word Problem

Question

The distance d that an object falls is directly proportional to the square of the time of the fall, t. A person who is parachuting for the first time is told to wait 16 seconds before opening the parachute. If the person falls 64 feet in 2 seconds, find how far he falls in 16 seconds.

 

Answer 1

Using the formula given we get

 

D = k T^2

 

Where d is the distance and k is the constant of proportionality. 

First find the value of k

 

64 = 4 k

 

K = 16

 

Now let's solve for t = 16

 

D = 16 (16^2)

 

= 256 × 16

 

= 4096 feet

 

That's your answer. 

Answer 2

Use the formula: d=kT^2, with:

d being the fallen distance at a certain time

k being the constant of variation

T being time taken to fall to a certain distance



We know it takes a certain time to fall a specific distance.  Thus:

 

64 = k(2^2) gives 16 for k because we know that the person falls 64 feet in 2 seconds.

 

Plug that back in and d = 16 *( 16 ^2) which means the distance is 4096 ft.