A stone is dropped from the upper observation deck of a tower, 650 m above the ground. (Assume g = 9.8 m/s2.)

Question

(a)

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

s(t) = 

 

(b)

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

 s

(c)

With what velocity does it strike the ground? (Round your answer to one decimal place.)

 m/s

(d)

If the stone is thrown downward with a velocity of 7 m/s, how long does it take to reach the ground? (Round your answer to two decimal places.)

 s

Answer 1

a)

s(t) =-4.9t^2 +650

b)

t^2 =650/4.9

t=sqr(650/4.9)=about 11.518= 11.5 seconds to hit the ground

c)

v(t)= s'(t) = -9.8t

v(11.5)= -9.8(11.5) = about-112.9 meters per second when it hits the ground

d)

s(t)= -4.9t^2-6t +650=0

t=6/-9.8 + (1/9.8)sqr(36+4(4.9)(650)) = time to hit the ground if thrown at 6 meters per second down

=10.92153 sec

t s(t)

0, 650

10 -490-60+650 = 110

10.9, 2.4 above ground

11 -2.9 below ground

10.9 seconds to hit ground, rounded off to nearest one decimal