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Citrus2011
6 days ago
12

An astronaut is standing on the surface of a planet that has a mass of 6.42×1023 kg and a radius of 3397 km. The astronaut fires

a 2.6-g bullet straight up into the air with an initial velocity of 406 m/s. What is the greatest height the bullet will reach? The planet has no atmosphere.
Physics
1 answer:
serg [2.5K]6 days ago
7 0
The final calculated height is 22.2 km. By converting 3397 km to meters, we achieve 3397000m. Using the gravitational constant, we compute the gravitational acceleration on the planet in accordance with Newton's law of gravitation, where M and R represent the planet's mass and radius, respectively. As the bullet ascends to its peak height, its kinetic energy transitions to potential energy. We account for the bullet mass and its initial velocity of 406 m/s, simplifying both sides of the equation to ultimately express the height reached as 22.2 km.
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A Honda Civic travels in a straight line along a road. The car’s distance x from a stop sign is given as a function of time t by
serg [2593]

a) Average velocity: 2.8 m/s

b) Average velocity: 5.2 m/s

c) Average velocity: 7.6 m/s

Explanation:

a)

The car's position over time t can be described by

x(t)=\alpha t^2 - \beta t^3

where

\alpha = 1.50 m/s^2

\beta = 0.05 m/s^3

To find the average velocity, we divide the displacement by the elapsed time:

v=\frac{\Delta x}{\Delta t}

At time t = 0, the position is:

x(0)=\alpha \cdot 0^2 - \beta \cdot 0^3 = 0

At time t = 2.00 s, the position is:

x(2)=\alpha \cdot 2^2 - \beta \cdot 2^3=5.6 m

This leads us to the displacement of

\Delta x = x(2)-x(0)=5.6-0=5.6 m

The duration for this interval is

\Delta t = 2.0 s - 0 s = 2.0 s

Therefore, the average velocity during this period is

v=\frac{5.6 m}{2.0 s}=2.8 m/s

b)

At time t = 0, the position is:

x(0)=\alpha \cdot 0^2 - \beta \cdot 0^3 = 0

At time t = 4.00 s, the position is:

x(4)=\alpha \cdot 4^2 - \beta \cdot 4^3=20.8 m

Thus, the displacement is

\Delta x = x(4)-x(0)=20.8-0=20.8 m

The time interval is

\Delta t = 4.0 - 0 = 4.0 s

This yields an average velocity of

v=\frac{20.8}{4.0}=5.2 m/s

c)

The position at t = 2 s is:

x(2)=\alpha \cdot 2^2 - \beta \cdot 2^3=5.6 m

And at t = 4 s it is:

x(4)=\alpha \cdot 4^2 - \beta \cdot 4^3=20.8 m

This gives us a displacement of

\Delta x = 20.8 - 5.6 = 15.2 m

While the time interval is

\Delta t = 4.0 - 2.0 = 2.0 s

So the resulting average velocity is

v=\frac{15.2}{2.0}=7.6 m/s

Find out more about average velocity:

6 0
1 month ago
A brick is dropped (zero initial speed) from the roof of a building. The brick strikes the ground in 1.90 s. You may ignore air
Sav [2226]

Answer:

Height (h) = 17 m

Velocity (v) = 18.6 m/s

Explanation: This problem can be solved using kinematic motion equations.

Given Data

Initial velocity (u) = 0

Acceleration (a) = g

Time (t) = 1.9 seconds

First, we calculate the height.

s=ut+0.5at^2\\h=ut+0.5at^2\\h=0*1.9+0.5*9.81*1.9^2\\h=17.707 m

Then, we find the final velocity

v=u+at\\v=0+9.81*1.9\\v=18.639

The acceleration graph is a linear representation described by y=9.8, as it remains constant:

The velocity graph can be represented by y=9.8x (where y signifies velocity and x indicates time):

The displacement graph can be described as y=4.9x^2 (with x as time and y as displacement):

These graphs apply exclusively from x=0 to x=1.9, so disregard other sections of the graphs.

5 0
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Softa [2029]
The required duration is 16.1 minutes. To determine the heat needed to raise the temperature, we must calculate the following amounts, where Q represents the required heat, m stands for mass, V represents the volume, C signifies specific heat, and ΔT indicates temperature change. After substituting the provided values into the formula and calculating, the next step is determining the required time based on the formula t = Q/P, where P is given as 1500 W. Ultimately, we find that the time needed is 16.1 minutes.
5 0
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A kangaroo jumps to a vertical height of 2.8 m. How long was it in the air before returning to earth
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The kangaroo reaches a maximum vertical altitude of 2.8 m, which can be calculated using the formula 2.8 = 1/2 * 9.8 * t^2. Thus, applying the equation s = ut + 1/2at^2.
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The final mass will be slightly lower due to evaporation. I learned this back in third grade, so it's surprising you're in high school and don't know this.
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27 days ago
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