1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Gnesinka [82]
3 years ago
8

A particle is projected with a velocity of

="40ms^-^1" align="absmiddle" class="latex-formula"> at an elevation of 60°. Calculate the vertical component of its velocity at a height of 50m. (Take g = 9.8ms^-^2)
A. 25\sqrt{3} ms^-^1\\\\B.20\sqrt{3} ms^-^1\\\\c. 2\sqrt{545} ms^-^1
Mathematics
1 answer:
Katena32 [7]3 years ago
3 0

Answer:

2\sqrt{55}\text{ m/s or }\approx 14.8\text{m/s}

Step-by-step explanation:

The vertical component of the initial launch can be found using basic trigonometry. In any right triangle, the sine of an angle is equal to its opposite side divided by the hypotenuse. Let the vertical component at launch be y. The magnitude of 40\text{ m/s} will be the hypotenuse, and the relevant angle is the angle to the horizontal at launch. Since we're given that the angle of elevation is 60^{\circ}, we have:

\sin 60^{\circ}=\frac{y}{40},\\y=40\sin 60^{\circ},\\y=20\sqrt{3}(Recall that \sin 60^{\circ}=\frac{\sqrt{3}}{2})

Now that we've found the vertical component of the velocity and launch, we can use kinematics equation v_f^2=v_i^2+2a\Delta y to solve this problem, where v_f/v_i is final and initial velocity, respectively, a is acceleration, and \Delta y is distance travelled. The only acceleration is acceleration due to gravity, which is approximately 9.8\:\mathrm{m/s^2}. However, since the projectile is moving up and gravity is pulling down, acceleration should be negative, represent the direction of the acceleration.

What we know:

  • v_i=20\sqrt{3}\text{ m/s}
  • a=-9.8\:\mathrm{m/s^2}
  • \Delta y =50\text{ m}

Solving for v_f:

v_f^2=(20\sqrt{3})^2+2(-9.8)(50),\\v_f^2=1200-980,\\v_f^2=220,\\v_f=\sqrt{220}=\boxed{2\sqrt{55}\text{ m/s}}

You might be interested in
Pherris is graphing the function f(x) = 2(3)x. He begins with the point (1, 6). Which could be the next point on his graph?
Savatey [412]

Answer: (2, 18)

Step-by-step explanation:

When x=2, f(2)=2(3)^{2}=18.

So, it should pass through (2, 18).

8 0
2 years ago
A produce supplier ships boxes of produce to individual customers. The distribution of weights of shipped boxes is approximately
schepotkina [342]

Answer:

0.67(4)+ 36

Option D

Step-by-step explanation:

Given that a producer ships boxes of produce to individual customers.(say x)

X is a normal random variable with mean = 36 and std dev  =4 lbs

By definition of std normal variate we know that

\frac{x-36}{4} is N(0,1)

75th percentile of std normal distribution is

0.675

Hence corresponding x would be

36+0.675(4)

Option D matches with this value

Hence answer is option D

0.67(4)+ 36

5 0
3 years ago
Read 2 more answers
Which is the median of the following data? 12,8,13,12,15,11,10,7
tensa zangetsu [6.8K]
11.5 beause you take the average of 12 and 11
7 0
3 years ago
pat is 12 years old James is 3 times as old as pat Raymond is 9 years younger than James. How old is raymond
Vsevolod [243]
I think the answer is 27 years old.
8 0
3 years ago
9x923 distributive property
Firlakuza [10]

Answer:

First break apart 923 into 900+20+3 then do 9 times 900,9 times 20 and 9 times 3. Then add all the products together to get your answer.

Step-by-step explanation:


8 0
3 years ago
Other questions:
  • How do you simplify 4 to the second power
    8·2 answers
  • Which is greater 1/4 of 12 or 1/3 of 12
    10·1 answer
  • Simply expression (-16)°
    5·2 answers
  • These data represent the volumes in cubic yards of the largest dams in the united states and in South America. Construct a boxpl
    5·1 answer
  • What is the lcm of 9 and 12<br><br>*lmc* lowest common multiple​
    9·1 answer
  • What are three different ways to make the number 15,638 with only hundreds, tens, and ones?
    8·2 answers
  • Pls pls pls help me with this
    7·1 answer
  • Use the table to work out the values of a , b , c , and d .​
    7·2 answers
  • URGENT PLEASE HELP !
    14·2 answers
  • What is the equation of the straight line shown below?
    8·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!