Physics, 08.11.2020 07:30 uniqueray33

A balloon is launched straight upward and has a hang time of 14 s. (wow) A.) What was the launching velocity of the balloon?
B.) How high did the balloon travel?
C.) How far did the balloon travel between t = 3 and t = 4 s?

Answers: 3

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Answers

Answer from: 2002babygurl

A) Vo = 137.34 [m/s]

B) Y = 961.38 [m]

C) y = 367.8[m] for t = 3 [s] and y = 470.88[m] for t = 4[s]

Explanation:

To solve this problem we must use the following equation of kinematics. We must keep in mind that the negative sign of the equation means that the acceleration of gravity acts in the opposite direction to the movement of the balloon.

$v_{f} =v_{o} -g*t$

where:

Vf = final velocity = 0 (the maximum hang time, maximum elevation)

Vo = initial velocity [m/s]

g = gravity acceleration = 9.81 [m/s²]

t = time = 14 [s]

0 = Vo - (9,81*14)

Vo = 137.34 [m/s]

Now we use the following equation.

$y=y_{o}+v_{o} *t -(\frac{1}{2} )*g*t^{2}$

where:

Yo = initial position = 0

Y = final position [m]

Vo = initial velocity = 137.34 [m/s]

Now replacing

Y = (137.34*14) - (0.5*9.81*14²)

Y = 961.38 [m]

With the above equation, we can calculate the distances between t = 3 and t = 4 [s]

$y=y_{o} +v_{o} *t - (1/2)*g*t^{2}$

y = (137.34*3) - (0.5*9.81*3²)

y = 367.8[m] for t = 3 [s]

for t = 4[s]

y = (137.34*4) - (0.5*9.81*4²)

y = 470.88[m]

Answer from: Quest

russian is not my first language, so i'm afraid i can't write out an answer in russian, but hopefully you can find a way to do so. here's my best translation of the problem: you're given a plot of a particle's position in one-dimensional space over time, and you're asked to find either the total distance traveled by the particle after 6 seconds had elapsed, or the total displacement of the particle after 6 seconds.

if you want the total distance traveled, you would first need to determine the particle's velocity as a function of time, then integrate that over the 6-second interval. we know the position function is quadratic with roots at 0 and 6, so we have

$x(t)=ax(x-6)$

where $a$ is unknown. because the position is parabolic, there is symmetry about the midpoint at $t=3$ , and we know that

$x(3)=10\implies -9a=10\implies a=-\dfrac{10}9$

so that the position function is

$x(t)=-\dfrac{10}9x(x-6)$

which means the velocity is

$v(t)=\dfrac{\mathrm dx}{\mathrm dt}=-\dfrac{20}9x+\dfrac{60}9$

then the total distance traveled is

$\displaystyle\int_{t=0}^{t=6}|v(t)|\,\mathrm dt=\left\{\int_{t-0}^{t=3}-\int_{t=3}^{t=6}\right\}v(t)\,\mathrm dt=20$

so the total distance traveled is 20 m.

on the other hand, if you want to find displacement: the particle starts at $x=0$ and ends at $x=0$ , so its displacement is 0.

Answer from: Quest

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A balloon is launched straight upward and has a hang time of 14 s. (wow) A.) What was the launching...