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3 years ago

15

Richard rides a bike on a road sloping downward and inclined at an angle of 30° with the horizontal. If he moves at a constant s

peed of 10 meters/second, calculate his vertical downward velocity.

1 answer:

arlik [135]3 years ago

8 0

Answer:

$v_y = 5\ m/s$

Explanation:

The vertical downward component of the speed of the bike can be simply found out by using the following geometric formula:

$v_y = vSin\theta$

where,

$v_y$ = vertical downward component of speed = ?

v = speed = 10 m/s

θ = angle of slope = 30°

Therefore,

$v_y = (10\ m/s)Sin\ 30^o\\v_y = 5\ m/s$

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3 years ago

A stereo speaker is rated at P1000 = 52 W of output at 1000 Hz. At 20 Hz, the sound intensity level LaTeX: \betaβ decreases by 1

baherus [9]

Answer:

The value of the power is $P_c = 38.55 \ W$

Explanation:

From the question we are told that

The power rating $P_{1000} =P_b= 52 \ W$

The frequency is $f = 1000 \ Hz$

The frequency at which the sound intensity decreases $f_k = 20 \ Hz$

The decrease in intensity is by $\beta = 1.3 dB$

Generally the initial intensity of the speaker is mathematically represented as

$\beta_1 = 10 log_{10} [\frac{P_b}{P_a} ]$

Generally the intensity of the speaker after it has been decreased is

$\beta_2 = 10 log_{10} [\frac{P_c}{P_a} ]$

So

$\beta_1-\beta_2 = 10 log_{10} [\frac{P_c}{P_a} ]- 10 log_{10} [\frac{P_b}{P_a} ]$

=> $\beta = 10 log_{10} [\frac{P_c}{P_a} ]- 10 log_{10} [\frac{P_b}{P_a} ]= 1.3$

=> $\beta =10log_{10} [\frac{\frac{P_b}{P_a}}{\frac{P_c}{P_a}} ] = 1.3$

=> $\beta =10log_{10} [\frac{P_b}{P_c} ] = 1.3$

=> $10log_{10} [\frac{P_b}{P_c} ] = 1.3$

=> $log_{10} [\frac{P_b}{P_c} ] = 0.13$

taking atilog of both sides

$[\frac{P_b}{P_c} ] = 10^{0.13}$

=> $[\frac{52}{P_c} ] = 10^{0.13}$

=> $P_c = \frac{52}{1.34896}$

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3 years ago

Convert 162 km/h into m/s.

patriot [66]

Answer:

45 m/s

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162 / 3.6 = 45 m/s

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