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Musya8 [376]
3 years ago
13

(20) A rocket is launched vertically. At time t = 0 seconds, the rocket’s engine shuts down. At the time, the rocket has reached

an altitude of 500m and is rising at a velocity of 125 m/s. Gravity then takes over. The height of the rocket as a function of time is h(t)=-9.8/2 t^2+125t+500,t>0. Using your function file from HW2A: Generate a plot of height (vertical axis) vs. time (horizontal axis) from 0 to 30 seconds. Include proper axis labels. Find the maximum height and the time at which it occurs: Analytically, showing your steps and equations. This part should be done entirely in the write-up: no coding Using the data cursor on the plot. Using the MAX function on your data from part (a) Using FMINSEARCH on your m file Comment on the differences between the methods. How closely does each method match the "true" (analytical) value? Find the time when the rocket hits the ground: Analytically, showing your equations. This part should be done entirely in the write-up: no coding Using the data cursor on the plot. Using FZERO on your m file Comment on the differences between the methods in each of part (B) and (C). How closely does each method match the "true" (analytical) value? Use a quantitative comparison to make your argument.

Physics
1 answer:
Diano4ka-milaya [45]3 years ago
3 0

Answer:

Explanation:

Given that,

h(t) = -9.8t² / 2 + 125t + 500

for t > 0.

At t = 0, the rocket is at height h = 500m, at a velocity of Vo = 125m/s.

We want to find the maximum height reached by rocket

Using mathematics maxima and minima

let find the turning point when dh/dt = 0

dh/dt = -9.8t + 125

dh / dt = 0 = -9.8t + 125

9.8t = 125

t = 125 / 9.8

t = 12.76s

Let find the turning point to know if this time t = 12.76 is maximum or minimum point

Let find d²h / dt²

d²h / dt² = -9.8

Since, d²h/dt² < 0, then, at t = 12.76s is the maximum points.

Then, the maximum height reached is

h =  -9.8t² / 2 + 125t + 500

h =  -9.8(12.76)² / 2 + 125(12.76) + 500

h = -797.80 + 1595 + 500

h = 1297.2 m

The maximum height reached is 1297.2 m

From the attachment, the maximum height is 1297.2m at t = 12.76sec.

Comment, the result are the same for both the analysis aspect and the graphical aspect.

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4.24m/s

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Answer:

\boxed {\boxed {\sf 100,000 \ Joules}}

Explanation:

Kinetic energy is energy due to motion. The formula is half the product of mass and velocity squared.

E_k= \frac{1}{2} mv^2

The mass of the roller coaster car is 2000 kilograms and the car is moving 10 meters per second.

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Substitute these values into the formula.

E_k= \frac{1}{2} (2000 \ kg ) \times (10 \ m/s)^2

Solve the exponent.

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E_k= \frac{1}{2} (2000 \ kg ) \times (100 \ m^2/s^2)

Multiply the first two numbers together.

E_k= 1000 \ kg  \times (100 \ m^2/s^2)

Multiply again.

E_k= 100,000 \ kg*m^2/s^2

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E_k= 100,000 \ J

The roller coaster car has <u>100,000 Joules</u> of kinetic energy.

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