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3 years ago

6

A 250 kg cannon containing a cannonball is initially at rest. If the cannon shoots the 20 kg cannonball at 15 m/s, what is the m

agnitude of the recoil velocity of the cannon?

1 answer:

vodomira [7]3 years ago

4 0

About 56 mph only for this tho it’s only for this one tho

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Wonder Woman and Superman fly to an altitude of 1690 km , carrying between them a chest full of jewels that they intend to put i

Arturiano [62]

Answer:

5120 m/s

Explanation:

The acceleration due to gravity is:

g = MG / r²

where M is the mass of the earth, G is the universal constant of gravitation, and r is the distance from the earth's center to the object's center.

Here, r = h + R, where h is the height of the chest above the surface and R is the radius of the earth.

g = MG / (h + R)²

Acceleration is the derivative of velocity:

dv/dt = MG / (h + R)²

Using chain rule, we can say:

(dv/dh) (dh/dt) = MG / (h + R)²

(dv/dh) v = MG / (h + R)²

Separate the variables:

v dv = MG / (h + R)² dh

Integrating:

∫₀ᵛ v dv = MG ∫₀ʰ dh / (h + R)²

½ v² |₀ᵛ = -MG / (h + R) |₀ʰ

½ (v² − 0²) = -MG / (h + R) − -MG / (0 + R)

½ v² = -MG / (h + R) + MG / R

½ v² = MGh / (R(h + R))

v² = 2MGh / (R(h + R))

Given:

M = 5.98×10²⁴ kg

R = 6.37×10⁶ m

h = 1.69×10⁶ m

G = 6.67×10⁻¹¹ m³/kg/s²

Plugging in:

v² = 2 (5.98×10²⁴) (6.67×10⁻¹¹) (1.69×10⁶) / ((6.37×10⁶) (1.69×10⁶ + 6.37×10⁶))

v² = 2 (5.98) (6.67) (1.69) / ((6.37) (1.69 + 6.37)) × 10⁷

v ≈ 5120 m/s

Notice that if we had approximated g as a constant 9.8 m/s², we would have gotten an answer of:

v² = v₀² + 2a(x - x₀)

v² = (0 m/s)² + 2 (9.8 m/s²) (1.69×10⁶ m - 0 m)

v ≈ 5760 m/s

So we know that our calculated velocity of 5120 m/s is a reasonable answer.

3 0

3 years ago

Archimedes' principle can be used to calculate the density of a fluid as well as that of a solid. suppose a chunk of iron with a

ella [17]

<span>(a) 39.5 g (b) 49.53 cm^3 (c) 0.7975 g/cm^3, liquid is an alcohol (a) This will be the difference between the weight of the iron in air and the weight submerged in fluid. So: 390.0 g - 350.5 g = 39.5 g (b) The density of iron is 7.874 g/cm^3, so the volume of the iron chunk is 390.0 g / 7.874 g/cm^3 = 49.53 cm^3 (c) The density of the fluid will be the mass of the fluid divided by the volume, so: 39.5 g / 49.53 cm^3 = 0.7975 g/cm^3 Since the density is very dependent upon the temperature and since the temperature wasn't specified, the actual substance can't be completely identified. Although some candidates are: 1. Mixture of Alcohol and water. Density ranges from 0.785 g/cm^3 to 1.000 g/cm^3. 2. Crude oil. Density 0.790 g/cm^3 3. Hydrazine. Density 0.795 g/cm^3 4. Methanol. Density 0.791 g/cm^3 5. Ocimene. Density 0.798 g/cm^3 The most likely candidate is a high concentration of an alcohol of some sort.</span>

5 0

3 years ago

A vector d has a magnitude of2.6 m and points north. What are the magnitudes and directions of the vectors (a) - d, (b) d/2.0, (

AleksandrR [38]

Solution :

A vector is defined as an element that has magnitude of some measure and direction.

It is given there is vector 'd' which has magnitude 2.6 m and its direction is towards north.

a). -d

The magnitude of the vector '-d' is 2.6 m and its direction is reversed, i.e. its direction is towards south.

b). d/2.0

The magnitude of the vector 'd/2.0' is 1.3 m and its direction is towards north.

c). - 2.5d

The magnitude of the vector increases by 2.5 times i.e. 2.5 x 2.6 = 6.5 m and the direction is towards south.

d). 5.0d

The magnitude of the vector increases by 5 times i.e. 5 x 2.6 = 13 m and the direction is towards north.

4 0

3 years ago

First, you will investigate purely vertical motion. The kinematics equation for vertical motion (ignoring air resistance) is giv

AlladinOne [14]

Answer: It takes 2.85 seconds.

Explanation: according to the question, the kinematics equation for vertical motion is

$y(t) = y_{0} + v_{0} .t - \frac{1}{2} .gt^{2}$

y₀ is the initial postion and equals 0 because it is fired at ground level;

v₀ is the initial speed and eqauls 14m/s;

g is gravity and it is 9.8m/s²;

y(t) is the final position and equals 0 because it is when the pumpkin hits the ground;

Rewriting the equation, we have:

0 + 14t - $\frac{1}{2}.9.8.t^{2}$ = 0

14t - 4.9t² = 0

t(14 - 4.9t) = 0

For this equation to be zero,

t = 0 or

14 - 4.9t = 0

- 4.9t = - 14

t = $\frac{14}{4.9}$

t = 2.86

It takes 2.86 seconds for the pumpkin to hit the ground.

6 0

3 years ago

Atoms gain the same electron configuration as noble gases by

Nesterboy [21]

Thr answer is D losing or gaining electons

3 0

3 years ago