1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
mario62 [17]
2 years ago
6

A car is parked on a steep incline, making an angle of 37.0° below the horizontal and overlooking the ocean, when its brakes fai

l and it begins to roll. Starting from rest at t = 0, the car rolls down the incline with a constant acceleration of 4.05 m/s2, traveling 46.5 m to the edge of a vertical cliff. The cliff is 30.0 m above the ocean. (a) Find the speed of the car when it reaches the edge of the cliff. m/s (b) Find the time interval elapsed when it arrives there. s (c) Find the velocity of the car when it lands in the ocean. magnitude m/s direction ° below the horizontal (d) Find the total time interval the car is in motion. s (e) Find the position of the car when it lands in the ocean, relative to the base of the cliff. m

Physics
1 answer:
patriot [66]2 years ago
5 0

Answer:

a) The speed of the car when it reaches the edge of the cliff is 19.4 m/s

b) The time it takes the car to reach the edge is 4.79 s

c) The velocity of the car when it lands in the ocean is 31.0 m/s at 60.2º below the horizontal

d) The total time interval the car is in motion is 6.34 s

e) The car lands 24 m from the base of the cliff.

Explanation:

Please, see the figure for a description of the situation.

a) The equation for the position of an accelerated object moving in a straight line is as follows:

x =x0 + v0 * t + 1/2 a * t²

where:

x = position of the car at time t

x0 = initial position

v0 = initial velocity

t = time

a = acceleration

Since the car starts from rest and the origin of the reference system is located where the car starts moving, v0 and x0 = 0. Then, the position of the car will be:

x = 1/2 a * t²

With the data we have, we can calculate the time it takes the car to reach the edge and with that time we can calculate the velocity at that point.

46.5 m = 1/2 * 4.05 m/s² * t²

2* 46.5 m / 4.05 m/s² = t²

<u>t = 4.79 s </u>

The equation for velocity is as follows:

v = v0  + a* t

Where:

v = velocity

v0 =  initial velocity

a = acceleration

t = time

For the car, the velocity will be

v = a * t

at the edge, the velocity will be:

v = 4.05 m/s² * 4.79 s = <u>19.4 m/s</u>

b) The time interval was calculated above, using the equation of  the position:

x = 1/2 a * t²

46.5 m = 1/2 * 4.05 m/s² * t²

2* 46.5 m / 4.05 m/s² = t²

t = 4.79 s

c) When the car falls, the position and velocity of the car are given by the following vectors:

r = (x0 + v0x * t, y0 + v0y * t + 1/2 * g * t²)

v =(v0x, v0y + g * t)

Where:

r = position vector

x0 = initial horizontal position

v0x = initial horizontal velocity

t = time

y0 = initial vertical position

v0y = initial vertical velocity

g = acceleration due to gravity

v = velocity vector

First, let´s calculate the initial vertical and horizontal velocities (v0x and v0y). For this part of the problem let´s place the center of the reference system where the car starts falling.

Seeing the figure, notice that the vectors v0x and v0y form a right triangle with the vector v0. Then, using trigonometry, we can calculate the magnitude of each velocity:

cos -37.0º = v0x / v0

(the angle is negative because it was measured clockwise and is below the horizontal)

(Note that now v0 is the velocity the car has when it reaches the edge. it was calculated in a) and is 19,4 m/s)

v0x = v0 * cos -37.0 = 19.4 m/s * cos -37.0º = 15.5 m/s

sin 37.0º = v0y/v0

v0y = v0 * sin -37.0 = 19.4 m/s * sin -37.0 = - 11. 7 m/s

Now that we have v0y, we can calculate the time it takes the car to land in the ocean, using the y-component of the vector "r final" (see figure):

y = y0 + v0y * t + 1/2 * g * t²

Notice in the figure that the y-component of the vector "r final" is -30 m, then:

-30 m = y0 + v0y * t + 1/2 * g * t²

According to our reference system, y0 = 0:

-30 m = v0y * t + 1/2 g * t²

-30 m = -11.7 m/s * t - 1/2 * 9.8 m/s² * t²

0 = 30 m - 11.7 m/s * t - 4.9 m/s² * t²

Solving this quadratic equation:

<u>t = 1.55 s</u> ( the other value was discarded because it was negative).

Now that we have the time, we can calculate the value of the y-component of the velocity vector when the car lands:

vy = v0y + g * t

vy = - 11. 7 m/s - 9.8 m/s² * 1.55s = -26.9 m/s

The x-component of the velocity vector is constant, then, vx = v0x = 15.5 m/s (calculated above).

The velocity vector when the car lands is:

v = (15.5 m/s, -26.9 m/s)

We have to express it in magnitude and direction, so let´s find the magnitude:

|v| = \sqrt{(15.5 m/s)^{2} + (-26.9 m/s)^{2}} = 31.0m/s

To find the direction, let´s use trigonometry again:

sin α = vy / v

sin α = 26.9 m/s / 31.0 m/s

α = 60.2º

(notice that the angle is measured below the horizontal, then it has to be negative).

Then, the vector velocity expressed in terms of its magnitude and direction is:

vy = v * sin -60.2º

vx = v * cos -60.2º

v = (31.0 m/s cos -60.2º, 31.0 m/s sin -60.2º)

<u>The velocity is 31.0 m/s at 60.2º below the horizontal</u>

d) The total time the car is in motion is the sum of the falling and rolling time. This times where calculated above.

total time = falling time + rolling time

total time = 1,55 s + 4.79 s = <u>6.34 s</u>

e) Using the equation for the position vector, we have to find "r final 1" (see figure):

r = (x0 + v0x * t, y0 + v0y * t + 1/2 * g * t²)

Notice that the y-component is 0 ( figure)

we have already calculated the falling time and the v0x. The initial position x0 is 0. Then.

r final 1 = ( v0x * t, 0)

r final 1 = (15.5 m/s * 1.55 s, 0)

r final 1 = (24.0 m, 0)

<u>The car lands 24 m from the base of the cliff.</u>

PHEW!, it was a very complete problem :)

You might be interested in
What primary element of light helps the observer see three-dimensions?
elixir [45]
<span>Shading. When light hits an opaque surface some is absorbed, the rest is reflected, The reflected light is called shading. Reflection is not simple and varies with material. The surface’s structure defines the details of reflection. Variations produce anything from bright specular reflection</span>
7 0
3 years ago
Read 2 more answers
What is the primary type of battery we use today to store energy?
Ahat [919]

Lithium-Ion batteries are commonly used in portable electronics and electric vehicles. These rechargeable batteries have two electrodes: one that's positively charged and contains lithium and another negative one that's typically made of graphite.

4 0
2 years ago
Read 2 more answers
How do you work out the potential diffrance
timurjin [86]

Answer:

The potential difference is the drop in voltage that occurs across a resistor as current flows through it in a circuit, potential difference or voltage(V) = current (I) *resistance (R), or to abbrevate V = I*R. In this case, I = 5amps and R = 10 ohms, so V = 5 * 10 = 50volts

6 0
2 years ago
A mother and daughter press their hands together and then push apart while ice skating. Immediately after they push away from ea
kherson [118]

Answer:

J

Explanation:

The daughter moves with greater acceleration backwards because of her weight.

7 0
2 years ago
Read 2 more answers
Find the net force for <br> 10 N<br> 10 N<br> 25degree<br> 5N<br> 5N
icang [17]

Answer:

30n

Explanation:

7 0
2 years ago
Other questions:
  • How do electromagnetism and gravitation differ from the strong and weak nuclear forces?
    11·1 answer
  • Thermodynamic Properties: Two identical, sealed, and well-insulated jars contain different gases at the same temperature. Each c
    12·1 answer
  • Hunk travelled 540 km at an average speed of 90 km/h. If Tim completed the same amount of distance with 1 hour and 30 min less t
    9·1 answer
  • A wave produced by a doorbell
    15·1 answer
  • If the density of an object is 30 g/cm3 and its volume is 10 cm3, what is its mass in grams?
    9·1 answer
  • Which two statements are true?
    10·2 answers
  • A straight wire in a magnetic field experiences a force of 0.026 N when the current in the wire is 1.5 A. The current in the wir
    7·1 answer
  • Consider going around a horizontal turn to the right. If the coaster suddenly slipped off the track, what path would it follow?
    13·1 answer
  • The diagram shows the electric field near conducting sphere a which of the following statements is correct
    15·1 answer
  • Draw the Free- Body diagram of the 37 kilogram glass falling to the floor in a vacuum.
    6·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!