Help solving problem

Question

projectile is launched upward with an initial velocity of 40 ft per second from the edge of a platform that is 56 feet above the ground. Use the function h(t)=-16t²+v₀t+s

Answer 1

It appears that you are trying to discover how long it will take a projectile launched from a 56 ft high platform with initial velocity of 40 ft/sec to hit the ground when the height is given by the function h(t) = -16t² + v₀t + 56

 

If so then you have a basic quadratic equation... 

 

-16t² + 40t + 56 = 0

We can reduce this equation by dividing everything by -8 since all our constants have a common factor

 

2t² - 5t - 7 = 0

 

using the quadratic equation  x = [-b +- sqrt(b² - 4ac)]/2a yields

 

t = [5 +- sqrt[25 - 4(2)(-7)]]/2(2)

 

t = [5 +- sqrt (25 + 56)]/4

 

t = [5 +- sqrt(81)]/4

 

t = (5 +- 9)/ 4

 

t = 14/4 seconds or t = -1/4 seconds

 

Since we know the time will not be the negative answer we discard t = -1/4 leaving

 

t = 14/4 seconds which can be reduced to t = 3 1/2 seconds

 

Thus the projectile would hit the ground at time t = 3 1/2 seconds