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Aloiza [94]
4 years ago
7

Students are studying the two-dimensional motion of objects as they move through the air. Specifically, they are examining the b

ehavior of a sphere that is launched horizontally from a location above the floor with an initial velocity vo in the +3 direction, as shown in the figure. The students assume that the positive directions are along the sphere's initial velocity for horizontal motion and downward for vertical motion.
The horizontal displacement of the object from its starting point is x, and the vertical displacement of the object from its starting point is y. One of the students derives an equation for y in terms of xx and other quantities. After examining the equation, the student claims that y is proportional to x^2.

Required:
Derive an equation for the vertical coordinate y of the sphere as a function of x, v0, and physical constants, as appropriate.
Physics
1 answer:
kupik [55]4 years ago
7 0

Answer:

   y = - (½ g / v₀²)   x²

Explanation:

This is a projectile launch exercise where there is no acceleration on the x-axis so

        x = v₀ₓ t

        v₀ₓ = v₀ cos tea

        y = v_{oy} t - ½ g t2

        v_{oy} = v₀ sin θ

as the sphere is thrown horizontally, the angle is tea = 0º, so the initial velocity remains

          v₀ₓ = v₀

           v_{oy} = 0

we substitute in our equations

          x = v₀ t

          y = - ½ g t²

we eliminate the time from these equations, we substitute the first in the second

      y = - ½ g (x / v₀)²

      y = - (½ g / v₀²)   x²

this is the equation of a parabola

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katrin [286]

C. The canoe's path will be a diagonal line from northeast to southwest.

Explanation:

We can solve this problem by using vector addition rules.

In fact, we know that:

- The velocity of the canoe has a component in the south direction, due to the velocity of the river which points towards south

- The canoe itself is trying to go from the eastern shore towards the western shore --> this means that the canoe has also a  component of the velocity in the west direction

This means that the resultant velocity of the canoe must be in a  direction intermediate between the directions of its two components: therefore, in the southwest direction.

Therefore, this means that

C. The canoe's path will be a diagonal line from northeast to southwest.

Learn more about vector addition:

brainly.com/question/4945130

brainly.com/question/5892298

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4 years ago
Consider a mass initially moving at 7.50 m/s. How does it take to move 3.5 km (Be sure to convert to meters) if it accelerates a
Tomtit [17]
The mass is moving by uniformly accelerated motion, with initial velocity v_i=7.50 m/s and acceleration a=0.55 m/s^2. Its position at time t is given by the following law:
x(t)=v_i t + \frac{1}{2}at^2
where we take the initial position x_i=0 since we are only interested in the distance traveled by the mass.

If we put x(t)=d=3.5 km=3500 m into the equation, the corresponding time t is the time it takes for the mass to travel this distance:
\frac{1}{2}at^2+v_it-d=0
4.9t^2+7.5t-3500 =0
And the two solutions for the equation are:
t=-25.5 s --> negative, we can discard it
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A marathon runner completes a 42.238 km course in 2 h, 31 min, and 46 s . There is an uncertainty of 29 m in the distance run an
icang [17]

Answer:

The percentage uncertainty in the average speed is 0.10% (2 sig. fig.)

Explanation:

Consider the formula for average speed \bar{v}.

\displaystyle \bar{v} = \frac{s}{t},

where

  • s is the total distance, and
  • t is the time taken.

The percentage uncertainty of a fraction is the sum of percentage uncertainties in

  • the numerator, and
  • the denominator.

What are the percentage uncertainties in s and t in this question?

The unit of the absolute uncertainty in s is meters. Thus, convert the unit of s to meters:

s = \rm 42.238\;km = 42.238\times 10^{3}\;m.

\begin{aligned}\displaystyle \text{Percentage Uncertainty in }s &= \frac{\text{Absolute Uncertainty in } s}{\text{Measured Value of }s}\times 100\% \\ &=\rm\frac{29\; m}{42.238\times 10^{3}\;m}\times 100\%\\ &= 0.0687\%\end{aligned}.

The unit of the absolute uncertainty in t is seconds. Convert the unit of t to seconds:

t = \rm 2\times 3600 + 31\times 60 + 46 = 9106\;s

Similarly,

\begin{aligned}\displaystyle \rm \text{Percentage Uncertainty in }t &= \frac{\text{Absolute Uncertainty in }t}{\text{Measured Value of }t}\times 100\% \\ &=\rm\frac{46\; s}{9106\;s}\times 100\%\\ &= 0.0329\%\end{aligned}.

The average speed \bar{v} here is a fraction of s and t. Both s and t come with uncertainty. The percentage uncertainty in \bar{v} will be the sum of percentage uncertainties in s and t. That is:

\text{Percentage Uncertainty in }\bar{v}\\=(\text{Percentage Uncertainty in } s) + (\text{Percentage Uncertainty in } t)\\ = 0.0687\% + 0.0329\%\\ = 0.010\%.

Generally, keep

  • two significant figures for percentage uncertainties that are less than 2%, and
  • one for those that are greater than 2%.

The percentage uncertainty in \bar{v} here is less than 2%. Thus, keep two significant figures. However, keep more significant figures than that in calculations to make sure that the final result is accurate.

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