A ball is thrown downward from the top of a cliff. The distance d, in feet, faLLaN BY THE BALL AFTER t seconds is molded by the equation d=16t^2+4t. How long .

Question

How long will it take the ball to fall a distance of 420 feet?  I am not sure how to write this out to solve. Think I am missing something. I know the answer is 5 Sec. but I cant make it work. thank you

Answer 1

d is the distance (in feet) and t is the time (in seconds).  d = 16t² + 4t.

 

You were given the distance (d) which is 420 and you are asked to look for how long (time, t)

 

Set the equation equal to 420.

 

420 = 16t² + 4t

 

You will see that it will be a quadratic equation because one of the t's is squared.  So to solve a quadratic equation you subtract 420 from both sides to get:

 

0 = 16t² + 4t - 420

 

See if there is a GCF of 16t² + 4t - 420 which is 4.  Divide everything by 4.

 

0 = 4t² + t - 105

 

See if it can be solved by factoring.

 

0 = (4t + 21)(t - 5)

 

Set each factor equal to zero.

 

4t + 21 = 0       t - 5 = 0

 

When you solve each equation, you will get t = -21/4 and t = 5.

 

And since there really is no such thing as negative time, the valid solution is t = 5.

 

5 seconds.