Question

A stone is thrown vertically upward at a velocity of 10 feet per second from a bridge that is 60 feet above the level of the water. The height h (in feet) of the stone at time t (in seconds) after it is thrown is given by

h = -16t2 + 10 + 60.

(a) Find the time when the stone is again 60 feet above the water. ____sec

(b) Find the time when the stone strikes the water. (Round your answer to two decimal places.) ____sec

(c) Does the stone reach a height of 90 feet? O Yes O No​

Answer 1

9514 1404 393

Answer:

(a) 0.625 seconds (rounds to 0.63)

(b) 2.27 seconds

(c) No

Explanation:

(a) We want to find t such that h = 60

60 = -16t^2 +10t +60

0 = t(-16t +10) . . . . . . . . . subtract 60, factor

t = 0 or t = 10/16 = 5/8 = 0.625

The stone is again 60 feet above the water after 0.625 seconds.

__

(b) We want to find t such that h = 0

0 = -16t^2 +10t +60

16t^2 -10t = 60

16(t^2 -5/8t +25/256) = 60 +25/16 . . . . complete the square

(t -5/16)^2 = 61.5625/16 = 3.84765625 . . . . simplify a bit

t = 5/16 +√3.84765625 ≈ 2.274 . . . . square root, add 5/16

The stone strikes the water at about 2.27 seconds.

__

(c) The equation above tells us the peak height of the stone is about 61.56 feet. It does not reach a height of 90 feet.