Matlab A rocket is launched vertically and at t-0, the rocket's engine shuts down. At that time, the rocket has reached an altitude of ho- 500 m and is rising at a velocity of to-125 m/s. Gravity then takes over. The height of the rocket as a function of time is: h(t)-ho+vot-gt², 120 where g -9.81 m/s². The time t-0 marks the time the engine shuts off. After this time, the rocket continues to rise and reaches a maximum height of Amax meters at time t-tmax. Then, it begins to drop and reaches the ground at time t-tg. a. Create a vector for times from 0 to 30 seconds using an increment of 2s. b. Use a for loop to compute h(t) for the time vector created in Part (a). e. Create a plot of the height versus time for the vectors defined in Part (a) and (b). Mark the z and y axes of the plot using appropriate labels. d. Noting that the rocket reaches a maximum height, Amax, when the height function, h(t), attains a maxima, compute the time at which this occurs, fax, and the maximum height, max. Also, display the results to the command window. Note that this is obtained by setting dh dt 0.

Matlab A rocket is launched vertically and at t-0, the rocket's engine shuts down. At that time, the rocket has reached an altitude of ho- 500 m and is rising at a velocity of to-125 m/s. Gravity then takes over. The height of the rocket as a function of time is: h(t)-ho+vot-gt², 120 where g -9.81 m/s². The time t-0 marks the time the engine shuts off. After this time, the rocket continues to rise and reaches a maximum height of Amax meters at time t-tmax. Then, it begins to drop and reaches the ground at time t-tg. a. Create a vector for times from 0 to 30 seconds using an increment of 2s. b. Use a for loop to compute h(t) for the time vector created in Part (a). e. Create a plot of the height versus time for the vectors defined in Part (a) and (b). Mark the z and y axes of the plot using appropriate labels. d. Noting that the rocket reaches a maximum height, Amax, when the height function, h(t), attains a maxima, compute the time at which this occurs, fax, and the maximum height, max. Also, display the results to the command window. Note that this is obtained by setting dh dt 0.

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Chapter1: Introduction

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Recurrence relation

A recurrence relation or recursive relation is an equation that represents a function in terms of the values of its smaller inputs. Every recurrence relation T(n) is a recursive function of integer n and consists of a base case and a recursive case.

Question

Matlab
A rocket is launched vertically and at t-0, the rocket's engine shuts down. At that time, the rocket
has reached an altitude of ho- 500 m and is rising at a velocity of to 125 m/s. Gravity then takes
over. The height of the rocket as a function of time is:
h(t)-ho+vot-gt², t20
where g -9.81 m/s². The time t-0 marks the time the engine shuts off. After this time, the rocket
continues to rise and reaches a maximum height of Amax meters at time t = tmax. Then, it begins to
drop and reaches the ground at time t = tg.
a. Create a vector for times from 0 to 30 seconds using an increment of 2 s.
b. Use a for loop to compute h(t) for the time vector created in Part (a).
e. Create a plot of the height versus time for the vectors defined in Part (a) and (b). Mark the
and y axes of the plot using appropriate labels.
d. Noting that the rocket reaches a maximum height, max, when the height function, h(t), attains
a maxima, compute the time at which this occurs, max, and the maximum height, max. Also,
display the results to the command window. Note that this is obtained by setting
dh
dt
-0.

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