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3 years ago

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Vectors vs Scalar

1 answer:

IrinaK [193]3 years ago

7 0

Answer:

I wish I knew

Explanation:

Ummm

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If a ball is thrown vertically upward from the roof of 32 foot building with a velocity of 64 ft/sec, its height after t seconds

stepan [7]

Answer:

a) $s_{max} = 96\,ft$ , b) $v(4.449\,s) = -78.368\,\frac{ft}{s}$

Explanation:

a) The maximum height is obtained with the help of the First and Second Derivative Tests:

First Derivative

$v(t) = 64 - 32\cdot t$

$64 - 32\cdot t = 0$

$t = 2\,s$

Second Derivative

$a(t) = -32$ (absolute maximum)

The maximum height reached by the ball is:

$s (2\,s) = 32 + 64\cdot (2\,s) - 16\cdot (2\,s)^{2}$

$s_{max} = 96\,ft$

b) The time required by the ball to hit the ground is:

$32+64\cdot t - 16\cdot t^{2} = 0$

$-16\cdot (t^{2}-4\cdot t - 2) = 0$

$t^{2}-4\cdot t - 2 = 0$

$(t -4.449)\cdot (t+0.449)\approx 0$

Just one root offers a solution that is physically reasonable:

$t = 4.449\,s$

The velocity of the ball when it hits the ground is:

$v(4.449\,s) = 64 - 32\cdot (4.449\,s)$

$v(4.449\,s) = -78.368\,\frac{ft}{s}$

6 0

3 years ago

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Four friends each took a different path walking from the drinking fountain to the cypress tree the table shows the distance that

lorasvet [3.4K]

Answer:

:)

Explanation:

5 0

3 years ago

A copper wire is 1.6 m long and its diameter is 1.1 mm. If the wire hangs vertically, how much weight (in N) must be added to it

qaws [65]

Answer:

Weight required = 194.51 N

Explanation:

The elongation is given by

$\Delta L=\frac{PL}{AE}$

Length , L= 1.6 m

Diameter, d = 1.1 mm

Area

$A=\frac{\pi d^2}{4}=\frac{\pi \times (1.1\times 10^{-3})^2}{4}=9.50\times 10^{-7}m^2$

Change in length, ΔL = 2.8 mm = 0.0028 m

Young's modulus of copper, E = 117 GPa = 117 x 10⁹ Pa

Substituting,

$\Delta L=\frac{PL}{AE}\\\\0.0028=\frac{P\times 1.6}{9.50\times 10^{-7}\times 117\times 10^9}\\\\P=194.51N$

Weight required = 194.51 N

8 0

3 years ago

incline plane is given length 12m,load 600 newton,effort 200 Newton, Height 3 metre find its velocity ratio and mechanical advan

Salsk061 [2.6K]

Answer:

i. The velocity ratio of the plane is 4.

ii. The mechanical advantage of the plane is 3.

Explanation:

i. The velocity ratio (VR) of an inclined plane is ratio of its length to the height. It is given as;

VR = $\frac{length of the plane}{height}$ = $\frac{l}{h}$

Given: l = 12 m, L = 600 N, E = 200 N, h = 3 m.

So that,

VR = $\frac{12}{3}$

= 4

The velocity ratio of the plane is 4.

ii. Mechanical advantage (MA) expresses the relationship between the load overcome to effort applied.

MA = $\frac{Load}{Effort}$ = $\frac{L}{E}$

= $\frac{600}{200}$

= 3

The mechanical advantage of the plane is 3.

Therefore, the velocity ratio of the inclined plane is 4, and its mechanical advantage is 3.

7 0

3 years ago

A 14000N car traveling at 25m/s rounds a curve of radius 200m. Find the following: a. The centripetal acceleration of the car.

tamaranim1 [39]

Answer:

Explanation:

Given

Weight of car $W=14,000\ N$

mass of car $m=\frac{14,000}{9.8}=1428.57\ N$

velocity of car $v=25\ m/s$

radius $r=200\ m$

(a)Centripetal acceleration is given by

$a_c=\frac{v^2}{r}$

$a_c=\frac{25^2}{200}$

$a_c=3.125\ m$

(b)Force that provide centripetal acceleration

$F=F_c=\frac{mv^2}{r}$

$F=\frac{1428.57\times 25^2}{200}$

$F=4464.285\ N$

(c)Friction force between car and tires is given by

$=\mu N$

where $\mu$ =coefficient of static friction

N=normal reaction

Centripetal force will balance the friction force

$F_c=F_r$

$4464.285=\mu \times 1428.57\times 9.8$

$\mu =0.318$

6 0

3 years ago

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