Explicit formula

Question

you visit the grand canyon and drop a penny off the edge of a cliff. The distance the penny will be from the top is 12 feet after one second, 48 feet after 3 seconds, and 102 feet after 6 seconds. Assuming an arithmetic sequence, write an explicit formula. Then determine the total distance the penny will fall in 13 seconds. If the cliff is 475 feet tall, how long does it take the penny to hit the ground?

Answer 1

Assuming the UNREALISTIC fact of arithmetic sequence.....

 

Terms would be

 

a₁ =12  for 1 second elapsed time...We'll have to assume that the series starts here!

_a2 = 12+d  for 2 seconds

a₃ = 12 + 2d = 48   for 3 seconds so d = 18

 

a_n = 12 +  (n-1)d for n seconds (represents total distance of fall)

 

When n=13, total distance would be 12 + (13-1)(18) = 12(1+18) = 12(19) = =228 ft. 

 

Set the a_n formula = 475 and solve for n, # of seconds to fall that distance.

 

REMEMBER, THIS IS NOT IN CONFORMITY TO THE PHYSICS PRINCIPLES that prevail on Earth.