Please complete parts E,F and G. Show all work and circle your answers. Problem #1 - Working for the latest Hollywood production, a brave stuntwoman in her car rides offthe horizontal surface of a cliff with an initial horizontal velocity of magnitude vi = 40.0 m/s and into the oceanwaters, as shown in the picture below. The edge of the cliff rises to a height H= 60.0 m above the water. Yourjob is to determine whether she will have enough time to leave the vehicle during flight, and whether she will beclose enough to the base of the cliff to be rescued if something goes wrong.Axa) What is vix, the (horizontal) x-component of the initial velocity vector v;?V Haizontal = V;40 mlsb) What is vi, the (vertical) y-component of the initial velocity vector vị?o mlsVertical =c) Find the time t that the car is in the air. Neglect air resistance for this and all the questions below.H= Vverticalt + 2 gt?60- Ot '2 x9.81メtt= 3.5sd) What is v&, the (horizontal) x-component of the final velocity vector vf (right before slamming into the water)?H=6 0mこ V:fx =40 m/sPage 2 of 7 e) Find the horizontal displacement Ax =xs-xi of the car from the base of the cliff at the time of impact with thesurface of the water.f) What is vf, the y-component of the final velocity vector v (right before slamming into the water)?tovo lon noie to sbutingmddi bai (g) What is the magnitude of the final velocity vector v (right before slamming into the water)?h) What angle Of does her car's trajectory make with the surface of the water right before impact? In other words,what angle (measured with respect to the + side of the x-axis) will her final velocity vector vr be pointed at?Of = tan -34, 310)4040.62Page 3 of 7

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Please complete parts E,F and G. Show all work and circle your answers.

Problem #1 - Working for the latest Hollywood production, a brave stuntwoman in her car rides off
the horizontal surface of a cliff with an initial horizontal velocity of magnitude vi = 40.0 m/s and into the ocean
waters, as shown in the picture below. The edge of the cliff rises to a height H= 60.0 m above the water. Your
job is to determine whether she will have enough time to leave the vehicle during flight, and whether she will be
close enough to the base of the cliff to be rescued if something goes wrong.
Ax
a) What is vix, the (horizontal) x-component of the initial velocity vector v;?
V Haizontal = V;
40 mls
b) What is vi, the (vertical) y-component of the initial velocity vector vị?
o mls
Vertical =
c) Find the time t that the car is in the air. Neglect air resistance for this and all the questions below.
H= Vvertical
t + 2 gt?
60- Ot '2 x9.81メt
t= 3.5s
d) What is v&, the (horizontal) x-component of the final velocity vector vf (right before slamming into the water)?
H=6 0m
こ V:
fx =40 m/s
Page 2 of 7

e) Find the horizontal displacement Ax =xs-xi of the car from the base of the cliff at the time of impact with the
surface of the water.
f) What is vf, the y-component of the final velocity vector v (right before slamming into the water)?
tovo lon noie to sbutingmddi bai (
g) What is the magnitude of the final velocity vector v (right before slamming into the water)?
h) What angle Of does her car's trajectory make with the surface of the water right before impact? In other words,
what angle (measured with respect to the + side of the x-axis) will her final velocity vector vr be pointed at?
Of = tan -
34, 310)
40
40.62
Page 3 of 7

Expert Solution

Step 1

Given,

Initial horizontal velocity, $u_{x} = 40 m / s$

Height of the cliff, H=60 m

(e.) Let us consider the horizontal distance travelled from the base of the cliff be x .

By equation of kinematics we have,

$x = u_{x} t + \frac{1}{2} a_{x} t^{2}$ .......(1)

The time taken to reach the water from the cliff is $t = 3.5 s [F r o m q u e s t i o n (c)]$

We know there is no acceleration in horizontal direction,

so $a_{x} = 0$

Thus equation (1) implies,

$x = 40 \times 3.5 + 0 \Rightarrow x = 140 m$

Thus, the horizontal distance travelled by the car before slamming the water is 140 m

Step 2

(f.) Initially the y-component of velocity is $u_{y} = 0 m / s$

Let $v_{y}$ be the y-component of final velocity

By equation of kinematics,

${v_{y}}^{2} = {u_{y}}^{2} + 2 g H \Rightarrow {v_{y}}^{2} = 2 \times 9.8 \times 60 \Rightarrow v_{y} = 34.29 m / s$

The y-component of final velocity before slamming the water is 34.29 m/s.

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