<span>et us assume that the origin is the floor right below the 30 ft. fence
To work this one out, we'll start with acceleration and integrate our way up to position.
At the time that the player hits the ball, the only force in action is gravity where: a = g (vector)
ax = 0
ay = -g (let's assume that g = 32.8 ft/s^2. If you use a different value for gravity, change the numbers.
To get the velocity of the ball, we integrate the acceleration
vx = v0x = v0cos30 = 103.92
vy = -gt + v0y = -32.8t + v0sin40 = -32.8t + 60
To get the positioning, we integrate the speed.
x = v0cos30t + x0 = 103.92t - 350
y = 1/2*(-32.8)t² + v0sin30t + y0 = -16.4t² + 60t + 4
If the ball clears the fence, it means x = 0, y > 30
x = 0 -> 103.92 t - 350 = 0 -> t = 3.36 seconds
for t = 3.36s,
y = -16.4(3.36)^2 + 60*(3.36) + 4
= 20.45 ft
which is less than 30ft, so it means that the ball will NOT clear the fence.
Just for fun, let's check what the speed should have been :)
x = v0cos30t + x0 = v0cos30t - 350
y = 1/2*(-32.8)t² + v0sin30t + y0 = -16.4t² + v0sin30t + 4
x = 0 -> v0t = 350/cos30
y = 30 ->
-16.4t^2 + v0t(sin30) + 4 = 30
-16.4t^2 + 350sin30/cos30 = 26
t^2 = (26 - 350tan30)/-16.4
t = 3.2s
v0t = 350/cos30 -> v0 = 350/tcos30 = 123.34 ft/s
So he needed to hit the ball at at least 123.34 ft/s to clear the fence.
You're welcome, Thanks please :)
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Answer:
(2, 5)
General Formulas and Concepts:
<u>Pre-Algebra</u>
Order of Operations: BPEMDAS
- Brackets
- Parenthesis
- Exponents
- Multiplication
- Division
- Addition
- Subtraction
Equality Properties
<u>Algebra I</u>
- Solving systems of equations using substitution/elimination
Step-by-step explanation:
<u>Step 1: Define Systems</u>
y - 3x = 1
2y - x = 12
<u>Step 2: Rewrite Systems</u>
y - 3x = 1
- Add 3x on both sides: y = 3x + 1
<u>Step 3: Redefine Systems</u>
y = 3x + 1
2y - x = 12
<u>Step 4: Solve for </u><em><u>x</u></em>
<em>Substitution</em>
- Substitute in <em>y</em>: 2(3x + 1) - x = 12
- Distribute 2: 6x + 2 - x = 12
- Combine like terms: 5x + 2 = 12
- Isolate <em>x</em> term: 5x = 10
- Isolate <em>x</em>: x = 2
<u>Step 5: Solve for </u><em><u>y</u></em>
- Define equation: 2y - x = 12
- Substitute in <em>x</em>: 2y - 2 = 12
- Isolate <em>y </em>term: 2y = 10
- Isolate <em>y</em>: y = 5
Divine the total number of the entire chart by the number of a single line or bar to give you the ratio in a bar or line chart. For example, if a bar or line represented 5 in a chart with a total of 30, you would divide 30 by 5. This would give you a result of 6. Therefore, the ratio would be 6:1.
Answer:
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