The height of an object after it is released can be modeled by the function f (t) = - 16t^2+vt+s, where t is the number of seconds after the object is released, v is the upward speed at release, and s is the starting height. If a quarterback throws a ball from his hand 6 feet in the air at a speed of 25 feet per second, how much time does his teammate have to catch the ball?

about 1.45 seconds

about 1.77 seconds

about 6 seconds

about 25 seconds

Question

Mathematics

Madelynn Huffman

23 June, 19:25

The height of an object after it is released can be modeled by the function f (t) = - 16t^2+vt+s, where t is the number of seconds after the object is released, v is the upward speed at release, and s is the starting height. If a quarterback throws a ball from his hand 6 feet in the air at a speed of 25 feet per second, how much time does his teammate have to catch the ball?

about 1.45 seconds

about 1.77 seconds

about 6 seconds

about 25 seconds

+2

Answers (1)

Know the Answer?

Irene Nash · Answer 1

Answer about 1.77 seconds.

f (t) = - 16 t^2 + 25t + 6

f (t) = height.

hieght = 0 = - 16t^2 + 25t + 6

Find t using the quadratic formula,

t = ( - 25 + / - √[25^2 - 4 (-16) (6) ]) / [2 * (-16) ]

t = [-25 + / - √ (625 + 384) ] / - 32

t = [-25 + / - 31.76] / - 32.

You will obtain two results one positive and one negative. Take the positive only as the other one has no physical meaning. t = 1.77 s.