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
MissTica
3 years ago
5

Doug hits a baseball straight towards a 15 ft high fence that is 400 ft from home plate. The ball is hit 2.5ft above the ground

and leaves the bat at an angle of 30∘ with the horizontal. Find the minimum initial velocity needed for the ball to clear the fence.
Mathematics
1 answer:
Scorpion4ik [409]3 years ago
5 0

Answer:

125.4\ \text{m/s}

Step-by-step explanation:

u = Initial velocity of baseball

\theta = Angle of hit = 30^{\circ}

x = Displacement in x direction = 400 ft

y = Displacement in y direction = 15 ft

y_0 = Height of hit = 2.5 ft

a_y = g = Acceleration due to gravity = 32.2\ \text{ft/s}^2

t = Time taken

Displacement in x direction

x=u_xt\\\Rightarrow x=u\cos\theta t\\\Rightarrow t=\dfrac{x}{u\cos\theta}\\\Rightarrow t=\dfrac{400}{u\cos30^{\circ}}\\\Rightarrow t=\dfrac{400}{u\dfrac{\sqrt{3}}{2}}\\\Rightarrow t=\dfrac{800}{u\sqrt{3}}

Displacement in y direction

y=y_0+u_yt+\dfrac{1}{2}a_yt^2\\\Rightarrow y=y_0+u\sin\theta t+\dfrac{1}{2}a_yt^2\\\Rightarrow 15=2.5+u\sin30^{\circ}(\dfrac{800}{u\sqrt{3}})+\dfrac{1}{2}\times -32.2\times (\dfrac{800}{u\sqrt{3}})^2\\\Rightarrow \dfrac{400}{\sqrt{3}}-\dfrac{10304000}{3u^2}-12.5=0\\\Rightarrow 218.44=\dfrac{10304000}{3u^2}\\\Rightarrow u=\sqrt{\dfrac{10304000}{3\times218.44}}\\\Rightarrow u=125.4\ \text{m/s}

The minimum initial velocity needed for the ball to clear the fence is 125.4\ \text{m/s}

You might be interested in
The sum of three numbers is 64. The second number is 3 more than the first. The third number is 11 less than twice the first. Fi
Cloud [144]
The first number: x
The second number: x + 3
The third number 2 * x - 11
Sum of all numbers: 65

We can write it down as an equation:

65 = x + 3 + x + 2x - 11
65 = 4x + 3 - 11
65 = 4x - 8                         / + 8 (both sides)
73 = 4x                             / ÷ 6 (both sides_
x = 18,25

Doublecheck:

The first number: 18,25
The second number 18,25 + 3 = 21,25
The third number: 2 * 18,25 - 11 = 36,5 - 11 = 25,5
Sum of all numbers: 18,25 + 21,25 + 25,25 = 65, so it's correct :)
8 0
3 years ago
Describe or show two ways to find the following product: 1 1/3x 2.
Alenkasestr [34]

1 and 1/3 time 2?  i thinks that's what you want?

or is it 1/3x squared?  

I;ll presume its 1 and 1/3 time 2

first way:

Multiple whole numbers first 1 x 2 = 2

Multiple fraction by the two  1/3 x 2 = 2/3

now add them together

2 and 2/3

second way

Make 1 and 1/3 improper = 4/3

make 2 into a  a/b form = 2/1  

now 4/3 x 2/1 = 8/3 now make a mixed number  2 and 2/3

8 0
3 years ago
Read 2 more answers
an angle measures 14° less than the measure of it's supplementary angle. what is the measure of each angle.​
Ipatiy [6.2K]

Answer:

(180-14):2= 166:2= 83° (smaller angle)

(180-14):2+14= 166:2+14= 83+14= 97° (bigger angle)

4 0
4 years ago
Factorize no i, l, o​
Mademuasel [1]

Answer:

here ,

question no. L the question is incomplete.

rest all are solved hope this helped u ☺️

3 0
3 years ago
4. If m23 = 54°, find each measure.
maks197457 [2]

Answer:

00PPI77yghhhhgtrrrr4tattereddoyouyouyouyouyouyouyouyouyouyouyouyouyouyouistheyouyouisghiiyyyyuiouuu

4 0
2 years ago
Other questions:
  • Suppose the height of a punt (in feet) after t seconds can be modeled by the function
    5·1 answer
  • 4(2x – 8) = 3(2 – Зх)​
    10·1 answer
  • Help me please ASAP!!!
    6·1 answer
  • Paula sold 35 packages of wrapping paper for this years booster club fundraiser. This is one less than twice the number of packa
    11·1 answer
  • 6 to the power of 2 add y to the power of 2 is r to the power of 2. what is r and y?
    13·1 answer
  • Help me out plzzzzzzzzzz!
    13·1 answer
  • Solve the right triangle below. Round all your answers to the nearest tenth. Measure of angle X = ______
    10·1 answer
  • I need help please explain
    8·2 answers
  • Pleaseee helppppp..will give 15 pts​
    5·1 answer
  • Question<br> Simplify: (-12az2-22³)+(-2a³ +7a²z)-(-4a²z+8az²).
    11·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!