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4 years ago

10

You and your friend are having a discussion about weight. He claims he weighs less on the 100th floor of a building that he does

on ground floor. Is he correct?

1 answer:

balu736 [363]4 years ago

7 0

No the acceleration of gravity on earth is still 9.8ms-2 unless he was on a different planet

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A baseball player hits a homerun, and the ball lands in the left field seats, which is 103m away from the point at which the bal

Sati [7]

(a) The ball has a final velocity vector

$\mathbf v_f=v_{x,f}\,\mathbf i+v_{y,f}\,\mathbf j$

with horizontal and vertical components, respectively,

$v_{x,f}=\left(20.5\dfrac{\rm m}{\rm s}\right)\cos(-38^\circ)\approx16.2\dfrac{\rm m}{\rm s}$

$v_{y,f}=\left(20.5\dfrac{\rm m}{\rm s}\right)\sin(-38^\circ)\approx-12.6\dfrac{\rm m}{\rm s}$

The horizontal component of the ball's velocity is constant throughout its trajectory, so $v_{x,i}=v_{x,f}$ , and the horizontal distance <em>x</em> that it covers after time <em>t</em> is

$x=v_{x,i}t=v_{x,f}t$

It lands 103 m away from where it's hit, so we can determine the time it it spends in the air:

$103\,\mathrm m=\left(16.2\dfrac{\rm m}{\rm s}\right)t\implies t\approx6.38\,\mathrm s$

The vertical component of the ball's velocity at time <em>t</em> is

$v_{y,f}=v_{y,i}-gt$

where <em>g</em> = 9.80 m/s² is the magnitude of the acceleration due to gravity. Solve for the vertical component of the initial velocity:

$-12.6\dfrac{\rm m}{\rm s}=v_{y,i}-\left(9.80\dfrac{\rm m}{\mathrm s^2}\right)(6.38\,\mathrm s)\implies v_{y,i}\approx49.9\dfrac{\rm m}{\rm s}$

So, the initial velocity vector is

$\mathbf v_i=v_{x,i}\,\mathbf i+v_{y,i}\,\mathbf j=\left(16.2\dfrac{\rm m}{\rm s}\right)\,\mathbf i+\left(49.9\dfrac{\rm m}{\rm s}\right)\,\mathbf j$

which carries an initial speed of

$\|\mathbf v_i\|=\sqrt{{v_{x,i}}^2+{v_{y,i}}^2}\approx\boxed{52.4\dfrac{\rm m}{\rm s}}$

and direction <em>θ</em> such that

$\tan\theta=\dfrac{v_{y,i}}{v_{x,i}}\implies\theta\approx\boxed{72.0^\circ}$

(b) I assume you're supposed to find the height of the ball when it lands in the seats. The ball's height <em>y</em> at time <em>t</em> is

$y=v_{y,i}t-\dfrac12gt^2$

so that when it lands in the seats at <em>t</em> ≈ 6.38 s, it has a height of

$y=\left(49.9\dfrac{\rm m}{\rm s}\right)(6.38\,\mathrm s)-\dfrac12\left(9.80\dfrac{\rm m}{\mathrm s^2}\right)(6.38\,\mathrm s)^2\approx\boxed{119\,\mathrm m}$

6 0

3 years ago

White light is spread out into its spectral components by a diffraction grating. If the grating has 1,970 grooves per centimeter

OlgaM077 [116]

Answer;

7.238°

Explanation

From question we know that the grating has 1,970 grooves per centimeter, we can convert to from (cm) to (nm) for unit consistency

The slit separation is expressed below

d=1cm/1970

d=0.0005076

=5076nm

Then the angle (in degrees) that the red light of wavelength 640 nm appear in first order can be calculated using expression below

Sin(x)= mλ/d

Where λ= wavelength=640 nm

d=slit separation

Sin(x)= mλ/d

Sin(x)=(1×640)/5076

=0.126

sin-1(0.126)

X= 7.238°

Therefore,the angle (in degrees) that the red light of wavelength 640 nm appear in first order is 7.238°

5 0

3 years ago

At the beach in San Francisco (0 meters) the pressure of the atmosphere is 101.325 kPa

Korvikt [17]

Answer:

$P = -\frac{17978}{1609344}(h)+101.325$

Explanation:

Given

$h = height$

$P = Pressure$

$(h_1,P_1) = (0,101.325)$

$(h_2,P_2) = (1609.344 ,83.437 )$

Required

Determine the linear equation for P in terms of h

First, we calculate the slope/rate (m);

The following formula is used:

$m = \frac{P_2 - P_1}{h_2 - h_1}$

Substitute values for P's and h's

$m = \frac{83.347 - 101.325}{1609.344- 0}$

$m = \frac{-17.978}{1609.344}$

$m = -\frac{17.978}{1609.344}$

Multiply by 1000/1000

$m = -\frac{17.978 * 1000}{1609.344*1000}$

$m = -\frac{17978}{1609344}$

The equation is then calculated using:

$P - P_1 = m(h - h_1)$

Substitute values for m, h1 and P1

$P - P_1 = m(h - h_1)$

$P - 101.325 = -\frac{17978}{1609344}(h - 0)$

$P - 101.325 = -\frac{17978}{1609344}(h)$

Make P the subject

$P = -\frac{17978}{1609344}(h)+101.325$

<em>The above is the required linear equation</em>

8 0

3 years ago

A steel aircraft carrier is 370 m long when moving through the icy North Atlantic at a temperature of 2.0 °C. By how much does t

34kurt

Answer:

The carrier lengthen is 0.08436 m.

Explanation:

Given that,

Length = 370 m

Initial temperature = 2.0°C

Final temperature = 21°C

We need to calculate the change temperature

Using formula of change of temperature

$\Delta T=T_{f}-T_{i}$

$\Delta T=21-2.0$

$\Delta T=19^{\circ}C$

We need to calculate the carrier lengthen

Using formula of length

$\Delta L=\alpha_{steel}\times L_{0}\times\Delta T$

Put the value into the formula

$\Delta L=1.2\times10^{-5}\times370\times19$

$\Delta L=0.08436\ m$

Hence, The carrier lengthen is 0.08436 m.

8 0

3 years ago

On the Apollo 14 mission to the moon, astronaut Alan Shepard hit a golf ball with a golf club improvised from a tool. The free-f

Sati [7]

On the moon, the gravitational acceleration is 1/6 of 9.8 m/s², so
g = 9.8/6 = 1.633 m/s²

Launch speed = 35 m/s
Launch angle = 27° above the horizontal.
Therefore,
The horizontal velocity is
u = 35*cos(27) = 31.1852 m/s
The vertical launch velocity is
v = 35*sin(27) = 15.8897 m/s

Part A
When the ball reaches maximum height, the time requires is given by
0 = v - gt
t = v/g = 15.8897/1.6333 = 9.7286 s
This is one half of the time of flight, which is
2*9.7286 = 19.457 s

Answer: 19.46 s (2 sig. figs)

8 0

4 years ago