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Alisiya [41]
3 years ago
15

A roofer drops a nail that hits the ground traveling at 26 m/s. How fast was the nail traveling 1 second before it hits the grou

nd?
Physics
1 answer:
ELEN [110]3 years ago
5 0
This problem can be solved using a kinematic equation. For this case, the following equation is useful:

v_final = v_initial + at

where,
v_final = final velocity of the nail
v_initial = initial velocity of the nail
a = acceleration due to gravity = 9.8 m/s^2
t = time 

First, we determine the time it takes for the nail to hit the ground. We know that the initial velocity is 0 m/s since the nail was only dropped. It has a final velocity of 26 m/s. We substitute these values to the equation and solve for t:

26 = 0 + 9.8*t
t = 26/9.8 = 2.6531 s

The problem asks the velocity of the nail at t = 1 second. We then subtract 1 second from the total time 2.6531 with v_final as unknown.

v_final = 0 + 9.8(2.6531-1) = 16.2004 m/s.

Thus, the nail was traveling at a speed of 16. 2004 m/s, 1 second before it hit the ground. 

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a. What proportion of resistors have resistances less than 90 Ω? b. Find the mean resistance. c. Find the standard deviation of
Anettt [7]

Answer:

a) 0.0625 = 6.25%

b) 106.67 Ω

c) 9.43 Ω

d) 1

Explanation:

The probability distribution is given as

f(x) = (x - 80)/800 for 80 < x < 120

f(x) = 0 otherwise.

f(x) = (x/800) - (0.1)

a) Proportion of resistors with resistance less than 90 Ω

P(X < 90) = ∫⁹⁰₈₀ f(x) dx

∫⁹⁰₈₀ f(x) dx = ∫⁹⁰₈₀ [(x/800) - (0.1)]

= [(x²/1600) - 0.1x]⁹⁰₈₀

= [(90²/1600) - 0.1(90)] - [(80²/1600) - 0.1(80)]

= (5.0625 - 9) - [4 - 8]

= -3.9375 + 4 = 0.0625 = 6.25%

b) The mean is given by the expected value expression E(X) = = Σ xᵢpᵢ (with the sum done all over the data set for each variable and its corresponding probability)

It can be written in integral form as

Mean = ∫¹²⁰₈₀ xf(x) dx (with the integral done all over the probability function, i.e. from, 80 to 120)

Mean = ∫¹²⁰₈₀ x[(x/800) - (0.1)] dx

= ∫¹²⁰₈₀ [(x²/800) - (0.1x)] dx

= [(x³/2400) - (0.05x²)]¹²⁰₈₀

= [(120³/2400) - (0.05(120²)] - [(80³/2400) - (0.05(80²)]

= [720 - 720] - [213.33 - 320] = 106.67 Ω

c) Standard deviation = √(variance)

Variance = Var(X) = Σx²p − μ²

μ = mean = expected value = 106.67 Ω

Σx²p = ∫¹²⁰₈₀ x²f(x) dx = ∫¹²⁰₈₀ x² [(x/800) - (0.1)] dx = ∫¹²⁰₈₀ [(x³/800) - (0.1x²)] dx

= [(x⁴/3200) - (0.0333x³)]¹²⁰₈₀

= [(120⁴/3200) - (0.0333(120³)] - [(80⁴/3200) - (0.0333(80)³)]

= (64800 - 57600) - (12800 - 17066.667)

= 11466.667

Variance = 11466.667 - 106.67² = 88.85

Standard deviation = √88.85 = 9.43 Ω

d) Cdf = sum of probabilities over the entire probability function

Cdf = ∫¹²⁰₈₀ f(x) dx = ∫¹²⁰₈₀ [(x/800) - (0.1)] dx

= [(x²/1600) - 0.1x]¹²⁰₈₀ = [(120²/1600) - 0.1(120)] - [(80²/1600) - 0.1(80)] = (9 - 12) - (4 - 8) = -3+4 = 1 as it should be!!!

Hope this Helps!!!

4 0
3 years ago
You should be able to use the speed of our fastest interplanetary spacecraft, and calculate the time in Days, it would take to t
Paul [167]
I think it would be 218 days!
8 0
3 years ago
What is the speed of a bobsled whose distance-time graph indicates that it traveled 100 m in 25 s?
larisa86 [58]

As per the question, the distance travelled by bobsled [s] = 100 m

The time taken by the bobsled to travel that distance [t] = 25 s

We are asked to calculate the speed of the bobsled.

The speed of the bobsled is calculated as -

                                            speed\ =\ \frac{distance}{time}

                                            v\ =\ \frac{s}{t}

                                                   =\frac{100\ m}{25\ s}

                                                   =\ 4\ m/s

Hence, the correct answer to the question is A. 4 m/s.  

8 0
3 years ago
You're collecting data in BeyondLabz for an object in free fall, subject to air resistance. How do you know when you've collecte
denis23 [38]

Enough data points would have been collected when specific data for upward and downward motion are collected.

<h3>What is a Data point?</h3>

A data point is a discrete unit of information. This information is always unique.

<h3>Free fall</h3>

An object subjected to free fall is under the influence of gravity. An object subjected has different time of motion for upward and downward motion.

Thus, we can conclude that enough data points would have been collected when specific data for upward and downward motion are collected.

Learn more about free fall here: brainly.com/question/10909077

6 0
2 years ago
How much work does a 120 watt motor perform for 300 seconds?
MrRa [10]

Answer:

36,000j

Explanation:

W= P•t

120•300= 36000

I checked my answer with P= W/t and got the right answer

hope this helps

6 0
2 years ago
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