An object is thrown downward with an initial velocity of 7 f

An object is thrown downward with an initial velocity of 7 feet per second. The relationship between the distance s it travels and time t is given by s = 7t + 16t^2. How long does it take the object to fall 78 feet? It takes seconds for the object to fall 78 feet.

Solution

equation of object is given by

s = 7t + 16t^2

time it takes to fall 78 feet

plug s = 78

78 = 7t + 16t^2

solving the equation for t

16t^2 + 7t - 78 = 0

( 16t + 39 ) ( t - 2) = 0

t = -39/16 , 2

discarding the negative value

t = 2

it takes 2 seconds to fall 78 feet