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Anna007 [38]
3 years ago
8

A small rock is thrown vertically upward with a speed of 22.0 m/s from the edge of the roof of a 30.0-m-tall building. The rock

doesn’t hit the building on its way back down and lands on the street below. Ignore air resistance. (a) What is the speed of the rock just before it hits the street? (b) How much time elapses from when the rock is thrown until it hits the street?
Physics
1 answer:
denis-greek [22]3 years ago
3 0

Answer:

a) v=32.74\frac{m}{s}.

b) t=\frac{v-v_0}{g} =5.58s.

Explanation:

a) What is the speed of the rock just before it hits the street?

From Kinematics we have v^2= v_0^2+2a(y_f-y_i).

If we take the top of the roof as the position y_0=0m, then

y_f=-30m and we have (also, a=g=-9.8\frac{m}{s^2}) :

v^2= v_0^2+ 2ay_f ⇒ v= \sqrt{v_0^2+ 2ay_f}

⇒ v=32.74\frac{m}{s}.

b) How much time elapses from when the rock is thrown until it hits the street?

From Kinematics we have v(t)=v_0+at=v_0+gt

When the rock touches the ground:

v=-32.74\frac{m}{s}

With a minus sign to indicate the vector velocity points down.

t=\frac{v-v_0}{g} =5.58s

(remember that g=-9.8\frac{m}{s^2})

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wo lacrosse players collide in midair. Jeremy has a mass of 120 kg and is moving at a speed of 3 m/s. Hans has a mass of 140 kg
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2.71 m/s fast Hans is moving after the collision.

<u>Explanation</u>:

Given that,

Mass of Jeremy is 120 kg (M_J)

Speed of Jeremy is 3 m/s (V_J)

Speed of Jeremy after collision is (V_{JA}) -2.5 m/s

Mass of Hans is 140 kg (M_H)

Speed of Hans is -2 m/s (V_H)

Speed of Hans after collision is (V_{HA})

Linear momentum is defined as “mass time’s speed of the vehicle”. Linear momentum before the collision of Jeremy and Hans is  

= =\mathrm{M}_{1} \times \mathrm{V}_{\mathrm{J}}+\mathrm{M}_{\mathrm{H}} \times \mathrm{V}_{\mathrm{H}}

Substitute the given values,

= 120 × 3 + 140 × (-2)

= 360 + (-280)

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Linear momentum after the collision of Jeremy and Hans is  

= =\mathrm{M}_{\mathrm{J}} \times \mathrm{V}_{\mathrm{JA}}+\mathrm{M}_{\mathrm{H}} \times \mathrm{V}_{\mathrm{HA}}

= 120 × (-2.5) + 140 × V_{HA}

= -300 + 140 × V_{HA}

We know that conservation of liner momentum,

Linear momentum before the collision = Linear momentum after the collision

80 = -300 + 140 × V_{HA}

80 + 300 = 140 × V_{HA}

380 = 140 × V_{HA}

380/140= V_{HA}

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2.71 m/s fast Hans is moving after the collision.

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Answer:

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The formula for discharge through a venturimeter is given as:

Q=C_d\frac{A_1A_2}{\sqrt{A_1^2-A_2^2}}\sqrt{2gh}

Where,

C_d is the coefficient of discharge = 0.97 (given)

A₁ = Area of the pipe

A₁ = \frac{\pi}{4}0.1^2 = 7.85\times 10^{-3}m^2

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Now,

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or

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or

Q = 29.28 ×10⁻³ m³/s

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