A projectile is shot from a cannon. The fixed parameters are the acceleration of gravity, g=9.8 m/sec2, and the muzzle velocity, v0=500 m/sec, at which the projectile leaves the cannon. The angle θ, in degrees, between the muzzle of the cannon and the ground can vary. The range of the projectile is
f(θ)=vo^2/g sin πθ/90=25510 sin πθ/90 meters.
Answers
The range at θ = 10⁰ is 155.4 meters.
What is a projectile?
A projectile is an object thrown or projected into the air, subject to gravity, following a curved trajectory.
Given that
v₀ = 500m/s
g = 9.8 m/s²
θ = 10⁰
Substitute into the function
f(θ)=v₀²/g sin πθ/90=25510 sin πθ/90 meters.
f(θ)= 25510sin πθ/90
= 25510sin10π/90
= 25510sinπ/9
= 25510sin(3.142/9)
= 25510sin(0.349)
= 25510 * 0.00609
= 155.4 m
The range at θ = 10⁰ is 155.4 meters.
Complete question
The greater the initial velocity of a projectile, the greater the range, with the maximum range achieved at a 45° angle in the absence of air resistance.
Explanation:The initial velocity of a projectile has a significant impact on its range. Specifically, the greater the initial speed, ℓ0, the greater the range. The formula for range R on level ground, neglecting air resistance, is given by R = (v0²/g) sin(2θ), where θ is the launch angle, v0 is the initial velocity, and g is the acceleration due to gravity. The maximum range is reached when the launch angle is 45°. With air resistance, the optimal angle decreases to roughly 38°. Additionally, for every angle other than the optimal, there are two different angles that yield the same range, and their sum totals 90°.
Related Questions
The price of gourmet coffee beans at the corner market has increased 10% per year over the past several years if the current cost is $40 per pound what did a pound of gourmet beans cost two years ago
Answers
Answer: $32.4
Step-by-step explanation:
Given : The price of gourmet coffee beans at the corner market has increased 10% (0.1) per year over the past several years.
The current cost is $40 per pound .
The exponential decay equation is given by :-
[tex]y=A(1-r)^x[/tex], where r is the rate of decay and A is the initial amount and x is the time period.
Put A = 40 , r= 0.1 and t=2, we get
[tex]y=40(1-0.1)^2=\$32.4[/tex]
Hence, the cost of a pound of gourmet beans two years ago= $32.4
Jonah is playing a video racing game called Checkpoint. The speed of Jonah’s car is recorded four times during one lap. At the first checkpoint, his speed is 80 miles per hour. At the second checkpoint, his speed has reduced by 5%. At the third checkpoint, Jonah’s speed has increased by the speed from the previous checkpoint. At the fourth checkpoint, his speed decreased by 20% compared with the third checkpoint. What is Jonah’s net change in speed between the first and fourth checkpoints?
Answers
Answer:
negative 15 is your answer
Step-by-step explanation:
the last number was negative so it would be negative 15
Answer:
-15
Step-by-step explanation:
yes
Graph the image of the given triangle after the transformation with the rule (x, y)→(x−1, y+2) . Select the "Polygon" button from the tool bar to plot your triangle. You may use the "Move" button to move the triangle after it is created. PolygonMove UndoRedoReset
Answers
Answer:
Hope this helps
Step-by-step explanation:
The cost of two mopeds is the same as the cost of seven bicycles. The cost of one bicycle is $152. Therefore, the cost of one moped is
Answers
1 bike = 152
7 bikes = 152*7 = 1064
1 moped = 1064/2 = $532
Soon after taking an aspirin, a patient has absorbed 320 mg of the drug. After 2 hours, only 80 mg remain. Find an exponential model for the amount of aspirin in the bloodstream after t hours.
Answers
[tex]\bf \textit{2 hours later, t = 2, the patient has 80mg in its blood} \\\\\\ 80=320(1-r)^2\implies \cfrac{80}{320}=(1-r)^2\implies \cfrac{1}{4}=(1-r)^2 \\\\\\ \sqrt{\cfrac{1}{4}}=1-r\implies \cfrac{\sqrt{1}}{\sqrt{4}}=1-r\implies \cfrac{1}{2}=1-r\implies r=1-\cfrac{1}{2} \\\\\\ r=\cfrac{1}{2}\implies r=0.5\qquad A=320(1-0.5)^t\implies \boxed{A=320(0.5)^t}[/tex]
A square poster has sides measuring 2 feet less than the sides of a square sign. If the difference between their areas is 32 square feet. Find the lengths of the sides of the poster and the sign?
Answers
Area of square two = [tex]x^2[/tex]
The difference of the area of two squares = 32
[tex]x^2-(x^2-4x+4)=32[/tex]
[tex]x^2-x^2+4x-4=32[/tex]
[tex]4x-4=32[/tex]
[tex]4x=32+4[/tex]
[tex]4x=36[/tex]
[tex]x=36/4[/tex]
[tex]x=9[/tex]
The side length of the poster = [tex]x-2 = 9-2 = 7 feet[/tex]
The side length of the sign = [tex]x=9[/tex]
Round 6,482 to the nearest ten hundred
Answers
what is 11.4 rounded to the nearest tenth
Answers
Rounded to the nearest tenth, 11.4 becomes 11.4.
When rounding a number to the nearest tenth, you look at the digit in the hundredths place.
If it's 5 or greater, you round up; if it's less than 5, you round down. In 11.4, the digit in the tenths place is 4, which is less than 5.
Therefore, 11.4 remains unchanged when rounded to the nearest tenth, resulting in 11.4.
This means the number stays the same, as it's already accurately represented to the nearest tenth without needing any adjustments.
Ms. Smith has 28 sixth graders and 35 seventh graders for math. If she wants to break the two grades into identical groups without any students left over, how many students will be in each group? Is it lcm or gcf?
Answers
Which equation represents a line that passes through (5, 1) and has a slope of ?
A. y – 5 = (x –1)
B. y – = 5(x –1)
C. y – 1 = (x –5)
D. y – 1 = 5
Answers
when you y -1 = ( x - 5)
1- 1 = 5 -5
0 = 0
where A y - 5 = ( x - 1)
1 - 5 = ( 5 - 1 )
-4 dosenot equal 4
What are the factors of 27
Answers
Note that two negative factors such as -3 and -9 can also multiply to equal 27.
anybody can help I need it by today at 4 pm please please please please please please help
Answers
The speeds have to be converted to km/min as well:
88 km/h = 88/60 km/min
76 km/h = 76/60 km/min
Let's define the location dimension x as x=0 at Town A, then x=976 in Town B.
With this we can set up two location equations:
Andy: x(t) = 88/60 t
Bernard: x(t) = 976 - 76/60 t
When they meet, the equations are equal, so we solve t for:
88/60 t = 976 - 76/60 t => t=510
Convert this number back to a clock time by adding 510 minutes to 9 AM, and you get 5:30 PM.
if five notebooks cost $5.25, how much would three notebooks cost?
Answers
$1.05*3 notebooks= $3.15 for 3 notebooks
Tony rounded each of the numbers 1,210 and 1,148 to the nearest hundred. Which choice correctly compares the rounded numbers?
Answers
The process of rounding numbers 1,210 and 1,148 to the nearest hundred results in 1,200 and 1,100, respectively. Therefore, 1,200 is greater than 1,100.
Explanation:In Mathematics, rounding numbers is common practice for simplifying calculations. We are given the numbers 1,210 and 1,148, and we need to round them to the nearest hundred.
Let's round them:
1,210 rounded to the nearest hundred is 1,200.1,148 rounded to the nearest hundred is 1,100.So, when comparing the rounded numbers, 1,200 is greater than 1,100.
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What are all the positive integers that are in the solution set for
m < 3
Answers
based on the census state A has 11 fewer electoral votes for president then state b. If the total number of electoral votes for these two states is 87 find the number for each state.
Answers
a = b - 11
b - 11 + b = 87
2b - 11 = 87
2b = 87 + 11
2b = 98
b = 98/2
b = 49 <===
a = b - 11
a = 49 - 11
a = 38 <===
HELP PLEASE,
Part a of the question was posted earlier on.
Answers
Where did the Maya's lived?
Thanks,
-Laura B
Answers
The Mayans lived, hmm, where is now know as Southern Mexico and northen Central America, including lots of countrys in their. etc, Guatemala, Belize, El Salvador
I hope this helps! :>
A jar of natural peanut butter normally cost four dollars today it's on sale for $3.60 what is the percentage of the discount
Answers
Tyron is making 52 cookies fi a party. Some will be pecan cookies. Some will be honey ginger cookies . The ratio of pecan to honey ginger cookies will be 7:6 . Suppose you use systematic guess and check to find the number of each type of cookie
Answers
Steps to divide 125.00 by 7.75
Answers
7.75 | 125
we want to get rid of that decimal....so we move it 2 spaces to the right....by doing that, we also have to move the decimal under the division sign by 2 spaces to the right....turning ur problem into :
16.1 R 225 <== ur answer
______
775 |12500.0
775
------- subtract
4750
4650
---------subtract
1000
775
-----------subtract
225
For a Circle of radius is 5 feet, find the arc length s subtended by a central angle of 42 degrees
Answers
The arc length subtended by a central angle of 42 degrees in a circle of radius 5 feet is 3.665 feet.
What is Circle?A circle is a shape consisting of all points in a plane that are at a given distance from a given point, the centre.
The formula for arc length is given by:
s = rθ
where s is the arc length, r is the radius of the circle, and θ is the central angle subtended by the arc in radians.
To use this formula, we first need to convert the central angle from degrees to radians:
θ = (π/180) × 42 = 0.733 radians
Now we can plug in the values of r and θ into the formula to get:
s = 5 × 0.733
= 3.665 feet
Therefore, the arc length subtended by a central angle of 42 degrees in a circle of radius 5 feet is 3.665 feet.
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A wall in Maria’s bedroom is in the shape of a trapezoid. The wall can be divided into a rectangle and a triangle.
Using the 45°-45°-90° triangle theorem, find the value of h, the height of the wall.
Answers
Using the 45°-45°-90° triangle theorem in a right triangle, where 'a' represents the triangle's leg that is also the trapezoid's height, 'h' equals 'a' and the hypotenuse is 'a' times √2. Additional information would be needed to solve for a numerical value of 'h'.
Explanation:In this problem, the wall's shape is a trapezoid, and we are using the 45°-45°-90° triangle theorem to find 'h', the height of the wall. We know in a 45°-45°-90° triangle, the two legs are congruent (same length), and the length of the hypotenuse is √2 times the length of a leg (based on Pythagorean theorem). In this case, if 'a' is the length of the triangle's leg connected to the rectangle, then 'h' would be equal to 'a' (since they are the legs in a 45-45-90 triangle), and the hypotenuse would be a√2.
Given an additional variable or measurement in this problem such as the length of the wall or the hypotenuse of the triangle, we could plug it in to solve for 'h'. Without additional information, the exact numerical height cannot be determined.
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if the perimeter of a rectangle is 318 inches, find the width and length. what's the answer?
Answers
let's consider that Length is n
Then width will be n+1
Perimeter of rectangle is equal to 2*(L+W) in this case
P = 2*(n + [n+ 1]) = 2*(n + n + 1) = 2(2n + 1)
P = 318
318 = 2(2n+1)
159 = 2n+1
159 - 1 = 2n
158 = 2n
79 = n
So this means that Length is 79 and Width is 80
or vice versa, Length is 80 and Width is 79
Select from the drop-down menu to correctly identify the property shown.
−4.8 + (3.2 + (−1.6)) = (3.2 + (−1.6)) + (−4.8)
A. Associative Property
B. Commutative Property
C. Opposite of a Sum Property
Answers
The answer is Commutative Property.
Answer:
Option B is correct.
Commutative property is used here.
Explanation:
Commutative Property states that we can add any number in any order, we will get the same result i.e, a+b = b+a.
let a = -4.8 and b = (3.2+(-1.6))
then, using commutative property we have;
a+b=b+a then,
−4.8 + (3.2 + (−1.6)) = (3.2 + (−1.6)) + (−4.8).
Create a process that will calculate the series 1 + x + x2 + x3 + x4 .......... + xn where x is a floating point number and n is a positive number. you process should be designed so exponentiation (or the pow function in c++) is not needed.
Answers
1. n is an integer.
2. Language is c++
double expr(double x, int n)
{
double sum = 0.0;
double power = 1.0; // Will have the value x^y where y ranges from 0 to n
int i;
for(i=0; i <= n; ++i) {
sum += power;
power *= x;
}
return sum;
}
Solve for x. 4−(2x+4)=5
A x=6
B x=−10
C x=−52
Answers
4 - 2x - 4 = 5
-2x = 5
x = - 5/2 <==
The solution for x in the equation 4 - (2x + 4) = 5 is x = -5/2. So, the correct choice is x = -5/2. Option c is the correct choice.
To solve for x in the equation 4 - (2x + 4) = 5, follow these steps:
1. First, simplify the equation by combining like terms. Start by removing the parentheses by distributing the negative sign:
4 - 2x - 4 = 5
2. Now, simplify further by combining the constants on the left side of the equation:
(4 - 4) - 2x = 5
0 - 2x = 5
3. Next, isolate the variable x by getting rid of the -2 coefficient. To do this, divide both sides of the equation by -2:
(0 - 2x) / -2 = 5 / -2
0 / -2 - (2x / -2) = -5/2
0 + x = -5/2
4. Finally, simplify:
x = -5/2
So, the solution for x is:
x = -5/2
So, Option c is the correct choice.
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Que. Solve for x. 4−(2x+4)=5
A x=6
B x=−10
C x=−5/2
Miguel score 35 fewer points in second bowling game than his first game his total score for the two games was 395 how many points did he score in each game? (plz show step by step)
Answers
his second game's score "b", and it was 35 fewer points, so is b=a - 35.
we also know that the total score for both games was 395, thus
[tex]\bf \begin{cases} a+\boxed{b}=395\\ a+\boxed{a-35}=395 \end{cases} \\\\\\ 2a-35=395\implies 2a=395+35\implies 2a=430\implies a=\cfrac{430}{2} \\\\\\ a=215[/tex]
how many did he score in the second game? well, b = a - 35.
What is the lateral area of the pyramid?
Answers
9*12.3 = 110.7
11*11.9 = 130.90
130.90 + 110.70 = 241.6 ft^2
Answer:
Step-by-step explanation:
Alright, lets get started.
The lateral area will be the area of all 4 sides.
The two sides have base length 11 feet and height of 11.9 feet.
The area of this side is : [tex]\frac{1}{2}*base*height[/tex]
The area of this side is : [tex]\frac{1}{2}*11*11.9=65.45[/tex]
The two sides have base length 9 feet and height 12.3 feet.
The area of this side is : [tex]\frac{1}{2}*9*12.3=55.35[/tex]
All 4 sides area will be : [tex]2(65.45+55.35)[/tex]
All 4 sides area = 241.6 square feet
Hence the lateral area will be 241.6 square feet : Answer B
Hope it will help :)
Jon bought 1 2⁄3 pounds of green peppers and 3⁄5 pound of yellow peppers. How much more did the green peppers weigh than the yellow peppers?
Answers
Re-write the problem as "subtract 3/5 from 5/3."
5 3
--- - -----
3 5
Note that the LCD here is (3)(5) = 15.
Multiply 5/3 by (15/15) and also multiply 3/5 by (15/15). Your result should be
25 9
------- - -----
15 15
Subtracting, we get 16/15. This is the answer. The green peppers weighed 16/15 lb, or 1 1/15 lb, more than did the other peppers.