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Oksana_A [137]
3 years ago
12

30 points please help a girl out! 

Physics
1 answer:
ziro4ka [17]3 years ago
5 0

the answer would have to be A tell me if im wrong



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astraxan [27]

Answer:

Range of the projectile: approximately 1.06 \times 10^{3}\; {\rm m}.

Maximum height of the projectile: approximately 80\; {\rm m} (approximately 45.0\; {\rm m} above the top of the cliff.)

The projectile was in the air for approximately 7.07\; {\rm s}.

The speed of the projectile would be approximately 155\; {\rm m \cdot s^{-1}} right before landing.

(Assumptions: drag is negligible, and that g = 9.81\; {\rm m\cdot s^{-1}}.)

Explanation:

If drag is negligible, the vertical acceleration of this projectile will be constantly a_{y} = (-g) = (-9.81)\; {\rm m\cdot s^{-2}}. The SUVAT equations will apply.

Let \theta denote the initial angle of elevation of this projectile.

Initial velocity of the projectile:

  • vertical component: u_{y} = u\, \sin(\theta) = 153\, \sin(11.2^{\circ}) \approx 29.71786\; {\rm m\cdot s^{-1}}
  • horizontal component: u_{x} = u\, \cos(\theta) = 153\, \cos(11.2^{\circ}) \approx 150.086\; {\rm m\cdot s^{-1}}.

Final vertical displacement of the projectile: x_{y} = (-35)\; {\rm m} (the projectile landed 35\: {\rm m} below the top of the cliff.)

Apply the SUVAT equation v^{2} - u^{2} = 2\, a\, x to find the final vertical velocity v_{y} of this projectile:

{v_{y}}^{2} - {u_{y}}^{2} = 2\, a_{y}\, x_{y}.

\begin{aligned} v_{y} &= -\sqrt{{u_{y}}^{2} + 2\, a_{y} \, x_{y}} \\ &= -\sqrt{(29.71786)^{2} + 2\, (-9.81)\, (-35)} \\ &\approx (-39.621)\; {\rm m\cdot s^{-1}}\end{aligned}.

(Negative since the projectile will be travelling downward towards the ground.)

Since drag is negligible, the horizontal velocity of this projectile will be a constant value. Thus, the final horizontal velocity of this projectile will be equal to the initial horizontal velocity: v_{x} = u_{x}.

The overall final velocity of this projectile will be:

\begin{aligned}v &= \sqrt{(v_{x})^{2} + (v_{y})^{2}} \\ &= \sqrt{(150.086)^{2} + (-39.621)^{2}} \\ &\approx 155\; {\rm m\cdot s^{-1}} \end{aligned}.

Change in the vertical component of the velocity of this projectile:

\begin{aligned} \Delta v_{y} &= v_{y} - u_{y} \\ &\approx (-39.621) - 29.71786 \\ &\approx 69.3386 \end{aligned}.

Divide the change in velocity by acceleration (rate of change in velocity) to find the time required to achieve such change:

\begin{aligned}t &= \frac{\Delta v_{y}}{a_{y}} \\ &\approx \frac{69.3386}{(-9.81)} \\ &\approx 7.0682\; {\rm s}\end{aligned}.

Hence, the projectile would be in the air for approximately 7.07\; {\rm s}.

Also the horizontal velocity of this projectile is u_{x} \approx 150.086\; {\rm m\cdot s^{-1}} throughout the flight, the range of this projectile will be:

\begin{aligned}x_{x} &= u_{x}\, t \\ &\approx (150.086)\, (7.0682) \\ &\approx 1.06 \times 10^{3}\; {\rm m} \end{aligned}.

When this projectile is at maximum height, its vertical velocity will be 0. Apply the SUVAT equation v^{2} - u^{2} = 2\, a\, x to find the maximum height of the projectile (relative to the top of the 35\; {\rm m} cliff.)

\begin{aligned}x &= \frac{{v_{y}}^{2} - {u_{y}}^{2}}{2\, a} \\ &\approx \frac{0^{2} - 29.71786^{2}}{2\, (-9.81)} \\ &\approx 45.0\; {\rm m}\end{aligned}.

Thus, the maximum height of the projectile relative to the ground will be approximately 45.0\; {\rm m} + 35\; {\rm m} = 80\; {\rm m}.

5 0
1 year ago
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