you have to solve for s. but s need to have two different answers

Question

The height h, in feet, of a ball above the ground t seconds after being thrown upward with a velocity of 64 ft/s is given by

h = −16t2 + 64t + 3.
After how many seconds will the ball be 51 ft above the ground? (Enter your answers as a comma-separated list.)

Answer 1

You are solving for t.  s is the unit for t, which is time.  Seconds is the unit of time.

 

Since we want to find the time it take for the ball to be 51 feet above the ground, set h=51.

 

51 = -16t² + 64t + 3

 

 

Subtract 51 on both sides of equation.

 

0 = -16t² + 64t - 48

 

 

Factor out a -16.

 

0 = -16(t² - 4t + 3)

 

0 = -16(t - 3)(t - 1)

 

t = 3   ,     t = 1

 

 

Only one of these solutions make sense.  1 second seems too short to be a reasonable answer.  That is like a quick blink of an eye.

 

 

We should go with 3 seconds.