College math word problem

Question

Suppose Juan and Pedro each throw a baseball into the air. The height of Juan’s baseball is given by h(t) = -16t2 +79t +6 , where h is in feet and t is in seconds. The height of Pedro’s baseball is given by the graph below:





Juan claims that his baseball went higher than Pedro’s, and Pedro says that his went higher.

a. Who is right? Explain your answer.

b. How long is each baseball airborne?

c. On a separate sheet of paper, copy the graph of Juan's throw and construct a graph of Pedro's throw as a function of time on the same set of axes. In the space below, explain how this can confirm your claim to parts (a) and (b)

Answer 1

To find the max, x = -b/2a

 

x = -7/-32 = 7/32

 

f(7/32) = -16(7/32)² + 79(7/32) + 6

 = 16(49/1024) + 553/32 + 6 = 784/1024 + 17,696/1024 + 6144/1024 = 24,624/1024 = 24.046875

 

Does Pedro's ball go higher than that?

 

When the balls hit the ground, y = 0. Solve for x when y = 0.