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Vadim26 [7]
3 years ago
11

A projectile fired at 5 m/s from a gun. If the horizontal component of the initial velocity is equal to 4 m/s. What is the value

of the vertical component?
Mathematics
1 answer:
svlad2 [7]3 years ago
5 0

Answer:

the  \: value \:  of  \: the \:  vertical  \: component \to : \\  (v_v) = 3m {s}^{ - 1}  \\

Step-by-step explanation:

let \: the \: velocity \: be \to \: v \\let \: the \: horizontal \: component \: be \to \: v_h \\ let \: the \: vertical \: component \: be \to \: v_v \\ applying \: the \: pythagorean \: rule \: of \: vectors \to :  \\  {v}^{2}  =  {v_v}^{2}  +  {v_h}^{2}  \\  {v_v}^{2}  =  {v}^{2}  - {v_h}^{2}  \\ {v_v}^{2} = {5}^{2}  - {4}^{2}  \\ v_v =  \sqrt{(25 - 16)}  \\ v_v =  \sqrt{9}  \\ \boxed{ v_v = 3 {ms}^{ - 1} }

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3x+9y=12 <br>-3x-6y=18 <br>Solve the system by using elimination​
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Answer:  (x, y) = (-26, 10)

This means x = -26 and y = 10 pair up together

===============================================================

How to get that answer:

Add the equations straight down. Think of having 3 separate columns for the three different like terms.

  • 3x + (-3x) becomes 0x and that's just 0. So the x terms go away
  • 9y + (-6y) is the same as 9y-6y which turns into 3y
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After all that, we're left with the simpler equation 3y = 30. That solves to y = 10 after dividing both sides by 3.

Plug this back into any equation involving x and y. Solve for x

3x+9y = 12

3x+9(10) = 12

3x+90 = 12

3x = 12-90

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x = -78/3

x = -26

We have found that x = -26 and y = 10 pair up together to form the solution.

-------------------

Checking the answer:

Plug (x,y) = (-26, 10) into the first equation

3x+9y = 12

3(-26)+9(10) = 12

-78+90 = 12

12 = 12

We get a true equation since the same thing is on both sides.

Repeat the same idea for the second equation

-3x-6y = 18

-3(-26) - 6(10) = 18

78 - 60 = 18

18 = 18

The second equation is true as well.

Both equations are true, so the solution (x, y) = (-26, 10) is confirmed.

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