College Algebra Word Problem

Question

The height h in feet of an object thrown upward from a height of 5 ft, with an initial velocity of 30 ft/sec, is given by the equation h=-16ft squared + 30t +5, where h represents the height of the object after t seconds. How long will it take the object to hit the ground? Answer in decimal form rounded to the nearest thousandth.

Answer 1

Take the height function,

 

h(t) = -16t² + 30t + 5,

 

set it equal to zero, and solve for t. One of the solutions will be negative (why?), but the other will be positive, and that's what you want for this question.

 

0 = -16t² + 30t + 5

 

t = (-30 ± √1220)/(-32)

 

After approximating,

 

t ≈ -0.154 or t ≈ 2.029 seconds.

 

The correct answer is the last one.