HW8_Solutions - hiarker(srh959 homework 08 Turner(58220...

hiarker (srh959) – homework 08 – Turner – (58220) 1
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001 (part 1 of 2) 10.0 points
A car is parked on a cliff overlooking the ocean
on an incline that makes an angle of 31 . 2
◦
below the horizontal. The negligent driver
leaves the car in neutral, and the emergency
brakes are defective. The car rolls from rest
down the incline with a constant acceleration
of 5 . 85 m / s
2
and travels 68 m to the edge of
the cliff. The cliff is 31 . 3 m above the ocean.
The acceleration of gravity is 9 . 8 m / s
2
.
Find the car’s position relative to the base
of the cliff when the car lands in the ocean.
Correct answer: 34 . 8252 m.
Explanation:
Given : a = 5 . 85 m / s
2
,
l = 68 m ,
h = 31 . 3 m , and
θ = 31 . 2
◦
.
The speed of the car when it reaches the
edge of the cliff is given by
v
2
= v
2
i
+ 2 a l = 2 a l
since v
i
= 0 m / s, so
v =
√
2 a ℓ
=
radicalBig
2 (5 . 85 m / s 2 ) (68 m)
= 28 . 2064 m / s .
Now, consider the projectile phase of the car’s
motion. The initial vertical velocity is
v
iy
= v sin θ
= (28 . 2064 m / s) sin(31 . 2
◦
)
= 14 . 6117 m / s .
and the vertical velocity with which the car
strikes the water is
v
2
y
= v
2
iy
+ 2 g h
= v
2
sin
2
θ + 2 g h
= (28 . 2064 m / s)
2
sin
2
31 . 2
◦
+ 2
(
9 . 8 m / s
2
)
(31 . 3 m)
= 826 . 981 m
2
/ s
2
,
so that
v
y
=
radicalBig
826 . 981 m 2 / s 2 = 28 . 7573 m / s .
To find the time of flight,
v
y
= v
iy
+ g Δ t
Δ t =
v
y
- v
iy
g
The initial horizontal velocity is v
ix
= v cos θ
and the horizontal motion of the car during
this time is
x = v
ix
Δ t
= ( v cos θ )
v
y
- v
iy
g
= (28 . 2064 m / s) cos 31 . 2
◦
×
(28 . 7573 m / s) - (14 . 6117 m / s)
(9 . 8 m / s 2 )
= 34 . 8252 m .
002 (part 2 of 2) 10.0 points
Find the length of time the car is in the air.
Correct answer: 1 . 44343 s.
Explanation:
Using the vertical motion,
v
y
= v
iy
+ g t
t =
v
y
- v
iy
g
=
(28 . 7573 m / s) - (14 . 6117 m / s)
(9 . 8 m / s
2
)
= 1 . 44343 s .
003 10.0 points
A soccer player kicks a rock horizontally off a
39 . 8 m high cliff into a pool of water.

hiarker (srh959) – homework 08 – Turner – (58220) 2
The acceleration of gravity is 9 . 8 m / s
2
.