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.
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hiarker (srh959) – homework 08 – Turner – (58220)
2
The acceleration of gravity is 9
.
8 m
/
s
2
.
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 Spring '09
 NUI
 Physics, Acceleration, Work, Velocity, Correct Answer, m/s, vy

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