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Papessa [141]
3 years ago
11

On Mars, where air resistance is negligible, an astronaut drops a rock from a cliff and notes that the rock falls about d meters

during the first t seconds of its fall. Assuming the rock does not hit the ground first, how far will it fall during the first 4t seconds of its fall?
Physics
2 answers:
Lana71 [14]3 years ago
8 0

The distance covered by the rock during the 4t seconds of its fall will be \fbox{16d}.

Explanation:

Given:

Distance covered by the rock in t\text{ sec} is d.

Concept:

As the astronaut drops the rock from the top of a cliff, the stone falls freely under the acceleration due to gravity of the Mars. This motion of the rock on the surface of the mass occurs according to the second equation of motion.

\boxed{S=v_it+\dfrac{1}{2}g_mt^2}

Here, S is the distance covered by the rock, v_i is the initial velocity of the rock, g_m is the acceleration due to gravity on the surface of Mars and t is the time for which the rock falls.

Since the rock is dropped from the top of the cliff, the rock will not have any initial velocity. So, the initial velocity of the rock will be zero.

Substitute the values in the given equation.

d=0(t)+\dfrac{1}{2}g_mt^2\\d=\dfrac{1}{2}g_mt^2

Now, in order to find the distance covered by the rock as it falls for time 4t, substitute 4t for t in the above expression.

\begin{aligned}d'&=0(t)+\dfrac{1}{2}g_m(4t)^2\\&=16.\dfrac{1}{2}g_mt^2\end{aligned}

Substitute d for \dfrac{1}{2}g_mt^2 in above expression.

d'=16.d

Thus, The distance covered by the rock during the 4t seconds of its fall will be \fbox{16d}.

Learn More:

1. Effect on the acceleration while sliding down the hill brainly.com/question/2286502

2. Expression for the acceleratuon of the block under friction brainly.com/question/6088121

3. Magnitude of acceleration of the car brainly.com/question/6423792

Answer Details:

Grade: High School

Subject: Physics

Chapter: Acceleration

Keywords:

Mars, cliff, stone, acceleration, gravity, falls, rock, top, time, t, 4t, distance, ground, equation of motion, initial velocity.

dimulka [17.4K]3 years ago
7 0

Answer:

d_1 = 16 d

Explanation:

As we know that initial speed of the fall of the stone is ZERO

v_i = 0

also the acceleration due to gravity on Mars is g

so we have

d = v_i t + \frac{1}{2}gt^2

now we have

d = 0 + \frac{1}{2}g t^2

now if the same is dropped for 4t seconds of time

then again we will use above equation

d_1 = 0 + \frac{1}{2}g(4t)^2

d_1 = 16(\frac{1}{2}gt^2)

d_1 = 16 d

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Se apunta un rifle horizontalmente con mira a un blanco pequeño que está a 200m en el suelo. La velocidad inicial de la bala es
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Lo importante a tener en cuenta sobre esta pregunta es que la velocidad horizontal de la bala no hace ninguna diferencia en cuanto al tiempo que tarda en caer al suelo.

Debido a que el arma no ha aplicado ninguna fuerza vertical a la bala, la única fuerza que afecta la bala es la gravedad. Esto significa que la bala tarda tanto en caer al suelo como lo haría si se cayera, a pesar de que ahora viaja una gran distancia horizontal en la duración.

Para encontrar el tiempo de viaje antes de tocar el suelo, tenemos 3 valores:

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-La velocidad inicial de la bala verticalmente. Como la bala es estacionaria verticalmente (solo viaja horizontalmente al inicio), u = 0m

Examinamos nuestras ecuaciones de movimiento, comúnmente conocidas como ecuaciones SUVAT. Es posible que necesite aprender estos para su examen, pero algunas tablas de examen los proporcionan.

Debido a que tenemos s, u y a, y estamos buscando el tiempo t, la ecuación relevante es

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Completando nuestros valores tenemos:

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1.5 = 4.905 x t ^ 2

Divide 1.5 entre 4.905 para encontrar t ^ 2

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