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lakkis [162]
2 years ago
13

Dump Tower is 96 stories tall. A small, 1.2-kg object is dropped over the side of the roof of the tower and accelerates toward t

he ground. The mass of the planet housing Dump Tower is 2.7 times the mass of Ganymede and the radius of the body is 1.7 times the radius of Makemake. You will track the object for its entire fall. Each story of this tower is 3.05 meters tall.
How many seconds will it take the object to reach the ground and what will be its impact speed with the ground?

The ball will not drop until your submit your answers.
Physics
1 answer:
sattari [20]2 years ago
8 0

Answer:

The time taken by the object to reach the ground, t = 25.04 / √gₓ

The final velocity of the object, v = 23.39 √gₓ

Explanation:

Given data,

The height of the Dump Tower, h = 96 x 3.05

                                                        = 292.8 m

The mass of the planet housing Dump Tower, M = 2.7 mₓ

The radius of the planet housing Dump Tower, R = 1.7 rₐ

The acceleration due to the gravity of the planet is,

                                        g = GM/R²

                                            = 2.7 Gmₓ / (1.7 rₐ)²

                                            = 0.934 Gmₓ/rₐ²

                                         g = 0.934 gₓ

Using the II equations of motion,

                       S = ut + ½ gt²

                          = 0 + ½ (0.934 gₓ) t²

                        t = √(2S/ 0.934 gₓ)

                           = √(2 x 292.8/ 0.934 gₓ)

                        t  = 25.04 / √gₓ

Hence, the time taken by the object to reach the ground, t = 25.04 / √gₓ

Using the I equations of motion

                       v = u + gt

                          = 0 + 0.934 gₓ (25.04 / √gₓ)

                        v  = 23.39 √gₓ

Hence, the final velocity of the object, v = 23.39 √gₓ

You might be interested in
Three people pull simultaneously on a stubborn donkey. Jack pulls eastward with a force of 80.5 N, Jill pulls with 81.7 N in the
Gnesinka [82]

Answer:

F = 233.52 N,  θ' = 351.41º

Explanation:

In this exercise we must find the net force applied on the donkey.

For this we use Newton's second law, where we create a reference frame with the horizontal x axis

let's decompose the forces

Jack

        = 80.5 N

Jill

       cos 45 = F_{2x} / F₂2

       sin 45 = F_{2y} / F₂2

       F_{2x} = F₂ cos 45

       F_{2y} = F₂ sin 45

       F_{2x} = 81.7 cos 45 = 57.77 N

       F_{2y} = 81.7 sin 45 = 57.77 N

Jane

      cos (270 + 45) = F_{3x} / F₃3

      sin 315 = F_{3y} / F₃

      F_{3x} = 131 cos 315 = 92.63 N

      F_{3y} = 131 sin 315 = -92.63 N

the force can be found in each axis

X axis

         F_{x} = F_{1x} + F_{2x} + F_{3x}

         F_{x} = 80.5 +57.77 + 92.63

         F_{x} = 230.9 N

Axis y

         F_{y} = F_{1y} + F_{2y} + F_{3y}

         F_{y} = 0 + 57.77 -92.63

         F_{y} = -34.86 N

we can give the result in two ways

a) F = (230.9 i ^ - 34.86 j ^) N

b) in the form of module and angle

we use the Pythagorean theorem

         F = √(Fₓ² + F_{y}²

        F = √(230.9² + 34.86²)

        F = 233.52 N

let's use trigonometry for the angle

        tan θ = \frac{F_y}{F_x} }

        θ = tan⁻¹ (\frac{F_y}{F_x} })

        θ = tan⁻¹ (-34.86 / 230.9)

        θ = -8.59º

if we measure this angle from the positive side of the x-axis counterclockwise

          θ' = 360 -θ

          θ‘= 360- 8.59

          θ' = 351.41º

5 0
2 years ago
A duck flies 60 m in 6 seconds what is the ducks speed? Show your work plz
Lana71 [14]

Answer:

Wouldn’t his or hers speed be 10m?

Explanation:

because 60 divided by 6 = 10

so 10m per second?

7 0
2 years ago
A 95.0 kg satellite moves on a circular orbit around the Earth at the altitude h=1.20*103 km. Find: a) the gravitational force e
Natali5045456 [20]

Answer:

a) F = 660.576\,N, b) a_{c} = 6.953\,\frac{m}{s^{2}}, c) v \approx 7255.423\,\frac{m}{s}, \omega = 9.583\times 10^{-4}\,\frac{rad}{s}, d) T \approx 1.821\,h

Explanation:

a) The gravitational force exerted by the Earth on the satellite is:

F = G\cdot \frac{m\cdot M}{r^{2}}

F = \left(6.674\times 10^{-11}\,\frac{m^{3}}{kg\cdot s^{2}} \right)\cdot \frac{(95\,kg)\cdot (5.972\times 10^{24}\,kg)}{(7.571\times 10^{6}\,m)^{2}}

F = 660.576\,N

b) The centripetal acceleration of the satellite is:

a_{c} = \frac{660.576\,N}{95\,kg}

a_{c} = 6.953\,\frac{m}{s^{2}}

c) The speed of the satellite is:

v = \sqrt{a_{c}\cdot R}

v = \sqrt{\left(6.953\,\frac{m}{s^{2}} \right)\cdot (7.571\times 10^{6}\,m)}

v \approx 7255.423\,\frac{m}{s}

Likewise, the angular speed is:

\omega = \frac{7255.423\,\frac{m}{s} }{7.571\times 10^{6}\,m}

\omega = 9.583\times 10^{-4}\,\frac{rad}{s}

d) The period of the satellite's rotation around the Earth is:

T = \frac{2\pi}{\left(9.583\times 10^{-4}\,\frac{rad}{s} \right)} \cdot \left(\frac{1\,hour}{3600\,s} \right)

T \approx 1.821\,h

6 0
3 years ago
What’s the difference between mechanical and chemical weathering
vampirchik [111]

Answer:

Mechanical weathering is the physical breakdown of rock into smaller pieces. Chemical weathering is the breakdown of rock by chemical processes.

Explanation:

Mechanical weathering (also called physical weathering) breaks rock into smaller pieces. These smaller pieces are just like the bigger rock, just smaller. That means the rock has changed physically without changing its composition. The smaller pieces have the same minerals, in just the same proportions as the original rock.

Chemical weathering is the other important type of weathering. Chemical weathering is different from mechanical weathering because the rock changes, not just in size of pieces, but in composition Chemical weathering works through chemical reactions that cause changes in the minerals.

5 0
3 years ago
Mass and energy are alternate aspects of a single entity called mass-energy. The relationship between these two physical quantit
Sever21 [200]

Answer:

Explanation:

ΔE = Δm × c^2

where,

ΔE = change in energy released with respect to change in mass

= 1.554 × 10^3 kJ

= 1.554 × 10^6 J

Δm = change in mass

c = the speed of light.

= 3 × 10^8 m/s

Equation of the reaction:

2H2 + O2 --> 2H2O

Mass change in this process, Δm = 1.554 × 10^6/(3 × 10^8)^2

= 1.727 × 10^-11 kg

The change in mass calculated from Einstein equation is small that its effect on formation of product will be negligible. Hence, law of conservation of mass holds correct for chemical reactions.

8 0
2 years ago
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