Question

(a) Find the velocity of the rock after two seconds.

(b) Find the velocity of the rock when t = a.

(c) When will the rock hit the surface? (Round your answer to one decimal place.)

t = ?


(d) With what velocity will the rock hit the surface?

Answer 1

y = 11t - 1.86 t^2 ;
y ' = 11 - 1.86 * 2 t ;
y ' = 11 - 3.72 t ;
y ' ( 1 ) = 7.28 ;
y' ( 2 ) = 3.56 ;
avg velcoity = ( 3.56 + 7.28 ) /2 = 5.42 <--------ans

Answer 2

Use h=-1/2(9.8)t^2+V0t
and v=-9.8t+V0

Answer 3

(a) Find the velocity of the rock after two seconds.
___m/s
we can assume that g on Mars is constant and Vi=0
then from Vavg = (Vf+Vi)/2
we get Vf = 2Vavg = 2(H/t)
so
H = 11t - 1.86t2. = 11(2) - 1.86(4) = 14.56 m
and
Vf = 2(28.56/2) = 14.56 m/s

(b) Find the velocity of the rock when t = a.
___ m/s
H = 11t - 1.86t^2. = 11a - 1.86a^2
so
Vf = 2(11a-1.86a^2)/a = 22 - 3.72a

(c) When will the rock hit the surface?
t = ____ seconds
when it comes back to surface, H=0
H = 11t - 1.86t^2
0 = 11t - 1.86 t^2
1.86t = 11
t = 5.91 s


(d) With what velocity will the rock hit the surface?
___ m/s
time up = time down
so from (c) time down = 1/2 time total = 2.95 s
and Hdown = -Hmax
Hmax = 11(2.95) - 1.86(2.95^2) = 16.26 m and Hdown= -16.19 m
then
Vavg = H/t = (Vf+Vi)/2 (and Vi = 0 at top of flight)
-16.19/2.95 = Vf/2
Vf = -10.97 m/s (negative means down)