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AVprozaik [17]
2 years ago
7

A 306 g cart moves on a horizontal, frictionless surface with a constant speed of 14.2 cm/s. A 76.3 g piece of modeling clay is

dropped vertically onto the cart. If the clay sticks to the cart, find the final speed of the system. Answer in units of cm/s.
Physics
1 answer:
faltersainse [42]2 years ago
4 0

To solve this problem it is necessary to apply the concepts related to the conservation of the momentum for an inelastic shock. Mathematically this can be described as

m_1v_1 + m_2v_2 = (m_1+m_2)V_f

Where,

m_{1,2} = Mass of each object

v_{1,2} = Initial velocity of each object

V_f = Final Velocity

If we assign the value of mass 1 and speed 1 to the cart and the variable of mass 2 to clay (which is at rest) we will have:

m_1v_1 + m_2v_2 = (m_1+m_2)V_f

(306)(14.2) + (76.3)(0) = (306+76.3)V_f

V_f = 11.36cm/s

Therefore the final speed of the system would be 11.36cm/s

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Answer:

In m/s^2:

a=11.3778 m/s^2

In units of g:

a=1.161 g

Explanation:

Since the racing greyhounds are capable of rounding corners at very high speed so we are going use the following formula of acceleration for circular paths.

a=\frac{v^2}{r}

where:

v is the speed

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Now,

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In g units:

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3 years ago
An archer fires an arrow at a castle 230 m away. The arrow is in flight for 6 seconds, then hits the wall of the castle and stic
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Answer:

(a). The initial speed of the arrow is 49.96 m/s.

(b). The angle is 39.90°.

Explanation:

Given that,

Horizontal distance = 230 m

Time t = 6 sec

Vertical distance = 16 m

We need to calculate the horizontal component

Using formula of horizontal component

R =u\cos\theta t

Put the value into the formula

\dfrac{230}{6} = u\cos\theta

u\cos\theta=38.33.....(I)

We need to calculate the height

Using vertical component

H=u\sin\theta t-\dfrac{1}{2}gt^2

Put the value in the equation

16 =u\sin\theta\times6-\dfrac{1}{2}\times9.8\times6^2

u\sin\theta=\dfrac{16+9.8\times18}{6}

u\sin\theta=32.06.....(II)

Dividing equation (II) and (I)

\dfrac{u\sin\theta}{u\cos\theta}=\dfrac{32.06}{38.33}

\tan\theta=0.8364

\theta=\tan^{-1}0.8364

\theta=39.90^{\circ}

(a). We need to calculate the initial speed

Using equation (I)

u\cos\theta\times t=38.33

Put the value into the formula

u =\dfrac{230}{6\times\cos39.90}

u=49.96\ m/s

(b). We have already calculate the angle.

Hence, (a). The initial speed of the arrow is 49.96 m/s.

(b). The angle is 39.90°.

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