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Gelneren [198K]
3 years ago
8

A student standing on a cliff that is a vertical height d = 8.0 m above the level ground throws a stone with velocity v0 = 24 m/

s at an angle θ = 21 ° below horizontal. The stone moves without air resistance; use a Cartesian coordinate system with the origin at the stone's initial position.
Part (a) With what speed, vf in meters per second, does the stone strike the ground 50%
Part (b) If the stone had been thrown from the clifftop with the same initial speed and the same angle, but above the horizontal would its impact velocity be different? YesNo Grade Summary 0% 100% Potential
Physics
1 answer:
PilotLPTM [1.2K]3 years ago
3 0

Answer:

a) Vf = 27.13 m/s

b) It would have been the same

Explanation:

On the y-axis:

Y=-Vo*sin\theta*t-1/2*g*t^2

-8=-24*sin(21)*t-1/2*10*t^2

Solving for t:

t1 = 0.67s     t2= -2.4s

Discarding the negative value and using the positive one to calculate the velocity:

Vf_y = -Vo*sin\theta-g*t

Vf_y = -15.3m/s

So, the module of the velocity will be:

Vf=\sqrt{(-15.3)^2+(24*cos(21))^2}

Vf=27.13m/s

If you throw it above horizontal, it would go up first, and when it reached the initial height, the velocity would be the same at the throwing instant. And starting then, the movement will be the same.

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Recall that

v_f=v_i+at

We have v_f=-v_i, so that

-2v_i=at\implies-2\left(8\,\dfrac{\mathrm m}{\mathrm s}\right)=\left(-2\,\dfrac{\mathrm m}{\mathrm s^2}\right)t\implies t=8\,\mathrm s

(b) The speed of the ball at the start and at the end of the roll are the same 8 m/s, so the average speed is also 8 m/s.

(c) The ball's average velocity is 0. Average velocity is given by \dfrac{v_i+v_f}2, and we know that v_f=-v_i.

(d) The position of the ball x_f at time t is given by

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Take the starting position to be the origin, x_i=0. Then after 6 seconds,

x_f=\left(8\,\dfrac{\mathrm m}{\mathrm s}\right)(6\,\mathrm s)+\dfrac12\left(-2\,\dfrac{\mathrm m}{\mathrm s^2}\right)(6\,\mathrm s)^2=42\,\mathrm m

so the ball is 42 m away from where it started.

We're not asked to say in which direction it's moving at this point, but just out of curiosity we can determine that too:

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Explanation:

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The given question is incomplete. The complete question is as follows.

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Explanation:

It is known that Boltzmann formula of entropy is as follows.

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where,   k = Boltzmann constant

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In the given case, W = 36. Now, we will put the given values into the above formula as follows.

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