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
The expression (m^2/m^1/3)^1/2 is equivalent to
Luda [366]
(m^2/m^1/3)^1/2
m^5/6
7 0
3 years ago
The complement of an angle is three times the measurement of the angle. Find the measurement of the larger angle.
olganol [36]
We know that two complements add up to 90.
Let's call the smaller angle x and the larger y.
3x = y
x + y = 90
We can use simple substitution.
x + 3x = 90
4x = 90
x = 22.5

Then, since we know that 3x=y, we can find the larger angle.
3*22.5 = 67.5
4 0
3 years ago
The graph of a proportional relationship is a straight line passing through the?​
Aneli [31]
Through the origin (0,0)
7 0
2 years ago
Read 2 more answers
On weekends a movie ticket costs $10.50. form an inequality and solve it to find the maximum number of tickets kate can buy with
Greeley [361]

$10.50

10 Tickets would be $105.00

$105.00 - $10.50 = $94.50 so 9 Tickets would be $94.50

$105.00 + $94.50 = $199.50

$205.00 - $199.50 = $5.50 which isn't enough for another ticket.

10 Tickets + 9 Tickets = 19 Tickets.

3 0
2 years ago
Identify the circumference of ⊙S in which A=64π ft^2. HELP ASAP!!
Vika [28.1K]

Answer:

C = 16π ft

Step-by-step explanation:

If we know the area

A = pi r^2

64 pi = pi r^2

Divide each side by pi

64 = r^2

Take the square root of each side

8 = r

The radius is 8

Now we can find the circumference

C = 2 *pi*r

C = 2*pi*8

C = 16pi

5 0
3 years ago
Read 2 more answers
Other questions:
  • Determine the solution set of (3x + 1)2 - 100 = 0.
    6·1 answer
  • Ollie used 852 heads to make 4 bracelets he put the same number of beads on each bracelet how many beads does each bracelet have
    9·2 answers
  • What is 15 3/5% as fraction in simplest form
    12·1 answer
  • Sam has 3 pieces of candy she gives away 2 candy's how much does she have?
    12·1 answer
  • What is 13 1/10 as a decimal
    13·2 answers
  • Find the derivative for the function.
    5·1 answer
  • HELP PLZZZZZZZZZZZZZZ
    11·1 answer
  • Help plzzzz I need the correct answers ASAP and that's my last marking period 4 and I'm in grade 12th
    7·1 answer
  • THIS IS WORTH 50 POINTS I will mark you as the brainlyest only if you graph this on a GRAPH. Graph this on a GRAPH y= 1/3x+3 .
    13·2 answers
  • 12 is 80% of what number ?
    10·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!