The equation s=16r^2+15t

Question

The equation s=16r^2+15t

 

gives the distance s in feet an object dropped off a building has descended in t seconds. Find the time t when the object has descended 25 feet. Round the answer to the nearest hundredth.

Answer 1

Set   s=25   and  solve for t.

 

25 = 16t² + 15t

 

 

Subtract 25 on both sides of the equation.

 

0 = 16t² + 15t - 25

 

 

Use quadratic formula to solve for t:

 

t = (-b ± √(b² - 4ac)) / 2a

 

where:

a = 16

b = 15

c = -25

 

Plug in these values into the formula.  You will get 2 t values.  Accept the positive of t.

Answer 2

I don't believe this equation is correct if an object were DROPPED off a building.  This formula implies that the object was thrown downward at 15 ft/sec initial velocity, and is also governed by Earth's gravity.

 

If the object were truly dropped, with 0 initial velocity, the linear term (15t) would not be present.

 

Discuss with your teacher!