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4 years ago

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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?

1 answer:

laiz [17]4 years ago

8 0

Answer:

6.0 s

98 m/s

Explanation:

The radius of the planet is much bigger than the height of the tower, so we will assume the acceleration is constant. Neglect air resistance.

Acceleration due to gravity on this planet is:

a = GM / r²

a = (6.67×10⁻¹¹ m³/kg/s²) (2.7 × 1.48×10²³ kg) / (1.7 × 750,000 m)²

a = 16.4 m/s²

The height of the tower is:

Δy = 96 × 3.05 m

Δy = 293 m

Given v₀ = 0 m/s, find t and v.

Δy = v₀ t + ½ at²

(293 m) = (0 m/s) t + ½ (16.4 m/s²) t²

t = 6.0 s

v² = v₀² + 2aΔy

v² = (0 m/s)² + 2 (16.4 m/s²) (293 m)

v = 98 m/s

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A world-class sprinter running a 100 m dash was clocked at 5.4 m/s 1.0 s after starting running and at 9.8 m/s 1.5 s later. In w

cupoosta [38]

Answer:

<em>The output power is greater in the interval from 1.0 s to 2.5 s</em>

Explanation:

<u>Physical Power </u>

It measures the amount of work W an object does in certain time t. The formula needed to compute power is

$\displaystyle P=\frac{W}{t}$

Work can be computed in several ways since we are given the motion conditions, we'll use this formula, for F= applied force, x=distance parallel to F

$W=F.x$

The second Newton's law gives us the net force as

$F=m.a$

being m the mass of the object and a the acceleration it has for a given period of time. In our problem, we have two different behaviors for each interval and we must calculate this force since the acceleration is changing. Let's calculate the acceleration in the first interval. We can use the formula for the final speed vf knowing the initial speed vo (which is 0 because the sprinter starts from rest), the acceleration a, and the time t:

$v_f=v_o+at$

$v_f=at$

Solving for a

$\displaystyle a=\frac{v_f}{t}={5.4}{1}$

$a=5.4\ m/s^2$

The distance traveled in the interval is given by

$\displaystyle x=v_o.t+\frac{a.t^2}{2}$

Since vo=0

$\displaystyle x=\frac{a.t^2}{2}=\frac{5.4(1)^2}{2}$

$x=2.7\ m$

The force is given by

$F=m.a$

We don't know the value of m, so the force is

$F=2.7m$

Computing the work done by the sprinter

$W=F.x=2.7m(5.4)$

$W=14.58m$

The power is finally computed

$\displaystyle P=\frac{W}{t}=\frac{14.58m}{1}$

$P=14.58m$

During the second interval, from t=1 sec to 1.5 sec, the speed changes from 5.4 m/s to 9.8 m/s. This allows us to compute the second acceleration

$\displaystyle a=\frac{v_f-v_o}{t}=\frac{9.8-5.4}{0.5}$

$a=8.8\ m/s^2$

The distance is

$\displaystyle x=(5.4).(0.5)+\frac{8.8(0.5)^2}{2}$

$x=3.8\ m$

The net force is

$F=m(8.8)=8.8m$

The work done by the sprinter is now computed as

$W=8.8m(3.8)=33.44m$

At last, the output power is

$\displaystyle P=\frac{33.44m}{0.5}=66.88m$

By comparing both results, and being m the same for both parts, we conclude the output power is greater in the interval from 1.0 s to 2.5 s

6 0

4 years ago

Two friends are walking on a hot beach on a hot summer day. one friend reports her feet are becoming hot she needs her sandals.

nata0808 [166]

Answer:

conduction

Explanation:

6 0

3 years ago

Jon recently drove to visit his parents who live 648 miles away. On his way there his average speed was 14 miles per hour faster

Vladimir79 [104]

Answer:

speed of the Jon visiting parents = 56 mph

speed of the Jon when returning from home = 56 - 14 = 42 mph

Explanation:

given,

distance of Jon parent's house = 648 mile

avg speed when he was visiting his parent's house be 'x' mph

avg speed when he is returning from his parent's house be 'x-14' mph

total time taken = 27 hours

total distance = speed × time

648 = x × t₁

$t_1 = \dfrac{648}{x}$

648 = ( x - 14 ) × t₂

$t_2 = \dfrac{648}{x-14}$

t = t₁ + t₂

$27 = \dfrac{648}{x} + \dfrac{648}{x-14}$

$1 = 24 (\dfrac{1}{x} + \dfrac{1}{x-14})$

x² - 62 x + 336 = 0

x² - 56 x - 6 x + 336 = 0

(x - 56 )(x - 6)=0

on solving

x = 56 ,6

hence, speed of the Jon visiting parents = 56 mph

speed of the Jon when returning from home = 56 - 14 = 42 mph

8 0

3 years ago

Read 2 more answers

What region of the atom determines the volume of the atom

NeX [460]

Hello kiddio!

Most of the mass<span> of atom is in a dense positively charged </span>nucleus<span>. Most of the volume of an atom is in an empty space in which negatively charged electrons move around the </span>nucleus<span>.
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4 years ago

A resistor converts 350 J of electrical energy to other forms of energy. What is the amount of

Helga [31]

Answer:

50C

Explanation:

Given parameters:

Electrical energy = 350J

Potential difference = 7V

Unknown:

Amount of charge = ?

Solution:

To solve this problem, use the expression below;

E = q x v

E is the electrical energy

q is the quantity of charge

v is the voltage

Insert the parameters and solve for q;

350 = q x 7

q = $\frac{350}{7}$

q = 50C

5 0

3 years ago