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oksian1 [2.3K]
3 years ago
11

. Explain why projectile motion, such as kicking a ball off the top of building, has a curved path. Identify the two forces invo

lved in your answer.
Mathematics
1 answer:
deff fn [24]3 years ago
4 0

The initial kick is the first force applied to the ball. It sends the ball up into the air (at some angle). If gravity wasn't present, then the ball would go upward forever in a straight line. However, gravity is the second force pulling down on the ball. This explains why the ball hits some peak point or highest point before it is pulled to the ground. Overall, the path the ball takes is a parabolic arch.

In short, the two forces are the initial kick and gravity.

side note: technically air resistance (aka air friction or drag) is a force being applied since the air pushes against the ball to slow it down, but often air resistance is really complicated and beyond the scope of many math courses. So your teacher may want you to ignore air resistance.

Another note: the initial kick is a one time force that only happens at the beginning. Once the ball is in the air, that force isn't applied anymore. In contrast, the force of gravity is always present and always pulling down. It's probably incredibly obvious, but it's worth pointing out this difference.

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Find the volume and area for the objects shown and answer Question
klio [65]

Step-by-step explanation:

You must write formulas regarding the volume and surface area of ​​the given solids.

\bold{\#1\ Rectangular\ prism:}\\\\V=lwh\\SA=2lw+2lh+2wh=2(lw+lh+wh)\\\\\bold{\#2\ Cylinder:}\\\\V=\pi r^2h\\SA=2\pi r^2+2\pi rh=2\pir(r+h)\\\\\bold{\#3\ Sphere:}\\\\V=\dfrac{4}{3}\pi r^3\\SA=4\pi r^2

\bold{\#4\ Cone:}\\\\V=\dfrac{1}{3}\pi r^2h\\\\\text{we need calculate the length of a slant length}\ l\\\text{use the Pythagorean theorem:}\\\\l^2=r^2+h^2\to l=\sqrt{r^2+h^2}\\\\SA=\pi r^2+\pi rl=\pi r^2+\pi r\sqrt{r^2+h^2}=\pi r(r+\sqrt{r^2+h^2})\\\\\bold{\#5\ Rectangular\ Pyramid:}\\\\V=\dfrac{1}{3}lwh\\\\

\\\text{we need to calculate the height of two different side walls}\ h_1\ \text{and}\ h_2\\\text{use the Pythagorean theorem:}\\\\h_1^2=\left(\dfrac{l}{2}\right)^2+h^2\to h_1=\sqrt{\left(\dfrac{l}{2}\right)^2+h^2}=\sqrt{\dfrac{l^2}{4}+h^2}=\sqrt{\dfrac{l^2}{4}+\dfrac{4h^2}{4}}\\\\h_1=\sqrt{\dfrac{l^2+4h^2}{4}}=\dfrac{\sqrt{l^2+4h^2}}{\sqrt4}=\dfrac{\sqrt{l^2+4h^2}}{2}

\\\\h_2^2=\left(\dfrac{w}{2}\right)^2+h^2\to h_2=\sqrt{\left(\dfrac{w}{2}\right)^2+h^2}=\sqrt{\dfrac{w^2}{4}+h^2}=\sqrt{\dfrac{w^2}{4}+\dfrac{4h^2}{4}}\\\\h_2=\sqrt{\dfrac{w^2+4h^2}{4}}=\dfrac{\sqrt{w^2+4h^2}}{\sqrt4}=\dfrac{\sqrt{w^2+4h^2}}{2}

SA=lw+2\cdot\dfrac{lh_1}{2}+2\cdot\dfrac{wh_2}{2}\\\\SA=lw+2\!\!\!\!\diagup\cdot\dfrac{l\cdot\frac{\sqrt{l^2+4h^2}}{2}}{2\!\!\!\!\diagup}+2\!\!\!\!\diagup\cdot\dfrac{w\cdot\frac{\sqrt{w^2+4h^2}}{2}}{2\!\!\!\!\diagup}\\\\SA=lw+\dfrac{l\sqrt{l^2+4h^2}}{2}+\dfrac{w\sqrt{w^2+4h^2}}{2}\\\\SA=\dfrac{2lw}{2}+\dfrac{l\sqrt{l^2+4h^2}}{2}+\dfrac{w\sqrt{w^2+4h^2}}{2}\\\\SA=\dfrac{2lw+l\sqrt{l^2+4h^2}+w\sqrt{w^2+4h^2}}{2}

6 0
2 years ago
The walls are rectangles with a height of 6 feet. A pint of paint covers about 50 square feet. How much paint do they need to pa
coldgirl [10]

Answer:

300

Step-by-step explanation:

4 0
2 years ago
A triangular prism and two nets are shown:
lilavasa [31]

Answer:

Net for the prism will have 3 rectangles with dimensions 5 by 15, 12 by 15 , and 13 by 15, and 2 triangles with legs 5 inches and 12 inches.

The correct net is net a.

Surface area = sum of areas of the three rectangles and sum of the two triangles.

SA = (5 x 15) + (12 x 15) + (13 x 15) + (5 x 12) = 75 + 180 + 195 + 60 = 510 square inches.

Step-by-step explanation:

Hope this helped

4 0
2 years ago
At the beginning of the semester students reported that they spend an average of 5 hours per day watching television, decreasing
Katyanochek1 [597]

Answer:

(a) X(t)=X(0)+\Delta X*t=5-0.5*t

(b) X(t)=X(0)+\Delta X*t=1+0.5*t

(c) At 4 weeks, when both will be seeing an average of 3 hours of TV.

Step-by-step explanation:

a) For the students, they start at X(0)=5 h and ΔX=-0.5 h/week.

We can write

X(t)=X(0)+\Delta X*t=5-0.5*t

b) For the professors, they start at X(0)=1 h and ΔX=+0.5 h/week.

We can write

X(t)=X(0)+\Delta X*t=1+0.5*t

c) The seew which they will be watching the same amount of hours will be the 4th week.

X(t)=5-0.5*t=1+0.5*t\\\\5-1=(0.5+0.5)*t\\\\t=4\, weeks

The amount of hours will be

x(4)=1+0.5*4=1+2=3\,hours

7 0
3 years ago
Which point would not be a solution to the system of linear inequalities shown below?
Bumek [7]

Answer:

C

Step-by-step explanation: looks right

dont  trust it though

4 0
2 years ago
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