CALCULUS HELP EMERGENCY TEST MONDAY

Question

A stone is dropped from the upper observation deck of a tower, 700 m above the ground. (Assume g = 9.8 m/s².)

(a) Find the initial values of the velocity v (in m/s) and the distance s (in meters) of the stone above the ground.

v(0)= 0 m /s

s(0)= 700 m

Find the velocity (in m/s) of the stone at time t.

v(t) =  −9.8t m/s

Find the distance (in meters) of the stone above ground at time t.

s(t) =  700−4.9t^2 m

(b) How long (in seconds) does it take the stone to reach the ground? (Round your answer to two decimal places.)

11.95 m/s

(c) With what velocity (in m/s) does it strike the ground? (Round your answer to one decimal place.)

-117.1 m/s

(d)If the stone is thrown downward with a velocity of 6 m/s, how long (in seconds) does it take to reach the ground? (Round your answer to two decimal places.)

 ???? s

The bolded things are my answers im pretty sure they right I just need help solving the last question (part d)

Answer 1

v(0) = -6 <-- because it is DOWNWARD, it is -6;

I could be wrong

s(0) = 700

a(t) = -9.8

v(t) = -9.8t + C

v(0) = -9.8(0)+C = -6 ---> C = -6

v(t) = -9.8t - 6

s(t) = -4.9t^2 - 6t + C

s(0) = 700 --> C = 700

s(t) = -4.9t^2 - 6t + 700

-4.9t^2 - 6t + 700 = 0

4.9t^2 + 6t - 700 = 0

x=11.3557 per quadratic formula

if I am wrong, then the quadratic comes out to be:

4.9t^2 - 6t - 700 = 0

which has solution 12.5802