The height of an object launched upward at a speed of 64 feet/second from a height of 80 feet is given by . How long will it take the projectile to hit the grou

Question

The height of an object launched upward at a speed of 64 feet/second from a height of 80 feet is given by . How long will it take the projectile to hit the ground?

Answer 1

The height of the projectile at time t is given by:

 

     h(t) = -16t² + 64t + 80

 

where -16 f/s² is the acceleration due to gravity, 64 f/s is the initial speed of the object and 80 f is the initial height.  When the object hits the ground, its height is zero, so:

 

     h(t) = -16t² + 64t + 80

     0 = -16t² + 64t + 80

     0 = t² - 4t - 5                  Divided both sides by -16

 

Solve for t by factoring.  You will get two answers, one positive and one negative.  The positive answer is the correct one since we can't go back in time.

 

Answer 2

h = 64t - 16t²

80 = 64t - 16t²

16t² - 64t + 80 = 0      Divide the whole equation by 16.

t² - 4t + 5 = 0

(t-5)(t+1) = 0

t - 5 = 0           or       t + 1 = 0

     t = 5 seconds               t = -1 seconds  (illogical)