Answer to Question #134467 in Algebra for js

Question

Karen is throwing an orange to her brother Saul, who is standing on the balcony of their home. The height h, in feet, of the orange above the ground t seconds after it is thrown is given by
h(t) = −16t2 + 32t + 5, 0 ≤ t ≤ 2.118.

If Saul's outstretched arms are 19 feet above the ground, will the orange ever be high enough so that he can catch it?

A. No. The orange will reach a maximum height of 10 feet.
B. No. The orange will reach a maximum height of 5 feet.
C. Yes. The orange will reach a maximum height of 21 feet.
D. There is not enough information given to answer the question.
E. Yes. The orange will reach a maximum height of 42 feet.

Answer 1

In any quadratic equation y= ax²+bx+c ,we can calculate the maximum height(y) of quadratic by putting the value of x=-b/2a in above equation... Here in our quadratic equation h(t)= -16t² +32t +5 , we have maximum height = h(-32/-32)=h(1) = -16+32+5= 21 feet. SO souls hand stretch is 19 feet above the ground ...till this height ball will pass through two times in their journey ... Hence Soul's stretched arm can catch the orange ... So answer will be "C. Yes. The orange will reach a maximum height of 21 feet."