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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}

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What is -1 29/40 as a decimal ? - show work plz:(
blagie [28]

Answer:

Step-by-step explanation:

A mixed number is an addition of its whole and fractional parts.

−(1 + 29/40)

Add

1 and 29/40

Write 1 as a fraction with a common denominator.

−(40/40 + 29/40)

Combine the numerators over the common denominator.

−40+29/40

Add 40 and 29

−69/40

The result can be shown in multiple forms.

Exact Form:−69/40

Decimal Form:−1.725

Mixed Number Form:−1 29/40

4 0
3 years ago
Read 2 more answers
Heidi solved the equation 3(x + 4) + 2 = 2 + 5(x – 4). Her steps are below: 3x + 12 + 2 = 2 + 5x – 20 3x + 14 = 5x – 18 14 = 2x
konstantin123 [22]
First, she distributed 3*x=3x , 3*4=12, 5*x= 5x, 5* -4= -20
Which gave her 3x+12+2=2+5x-20
Then, she combined like terms 12+2=14 and 2+ -20 = -18
Which gave her 3x+14=5x-18
Then, she subtracted 3x from both sided 
Which gave her 14=2x-18
Then, she added 18 to both sides
Which gave her 32=2x
And finally sh edivided 32 by 2 and got 16=x
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5 0
3 years ago
Read 2 more answers
If a ball is thrown in the air with a velocity 52 ft/s, its height in feet t seconds later is given by y = 52t - 16t^2. Find the
Sunny_sXe [5.5K]

Answer:

a.) -20ft/s

b.) -13.6ft/s

c.) -12.8ft/s

d.) -12.16ft/s

e.) -12ft/s

Step-by-step explanation:

Average Velocity = Change in distance/change in time.

Distance from the question in given in form of t as y= 52t - 16t² If our initial time is 2, distance travelled at t=2 is given as

Y(2) = 52(2) - 16(2)² =104 - 64

Y = 40ft.

For question a, when change In t is 0.5 seconds, that is from 2 sec to 2.5 seconds,

Average velocity = y(2.5) - y(2)/0.5

y(2.5) = 52(2.5) - 16(2.5)² =130 - 100 = 30

Y(2) = 40

Average velocity in 0.5 seconds = [30 - 40]/0.5 = -20ft/s.

For question b, when change In t is 0.1 seconds, that is from 2 sec to 2.1 seconds,

Average velocity = y(2.1) - y(2)/0.1

y(2.1) = 52(2.1) - 16(2.1)² =109.2 - 70.56= 38.64

Y(2) = 40,

Average velocity in 0.1 seconds = [38.64 - 40]/0.1 = -13.6ft/s.

For question c, when change In t is 0.05 seconds, that is from 2 sec to 2.05 seconds,

Average velocity = y(2.05) - y(2)/0.05

y(2.05) = 52(2.05) - 16(2.05)² = 106.6 - 67.24 = 39.36

Y(2) = 40

Average velocity in 0.05 seconds = [39.36 - 40]/0.05 = -12.8ft/s.

For question d, when change In t is 0.01 seconds, that is from 2 sec to 2.01 seconds,

Average velocity = y(2.01) - y(2)/0.01

y(2.01) = 52(2.01) - 16(2.01)² = 104.52 -64.6416 = 39.8784

Y(2) = 40

Average velocity in 0.5 seconds = [39.8784 - 40]/0.01 = -12.16ft/s.

Instantaneous velocity at t =2 is derived by getting the first derivative of y and inserting Our value of t=2 into the first derivative.

If y = 52t - 16t², then derivative of y becomes y' given as

y'= 52 - 32t

At t = 2,

y'= 52 - 32(2) = 52 - 64 = - 12ft/s.

Instantaneous velocity at t=2 is given as -12ft/s.

5 0
3 years ago
Ayo runs a fairground game.In each turn, a player rolls a fair dice numbered 1 - 6 and spins a fair spinner numbered 1 - 12.It c
aksik [14]

Using the definition of expected value, it is found that Ayo can be expected to make a profit of £55.8.

The <em>expected value</em> is given by the <u>sum of each outcome multiplied by it's respective probability.</u>

In this problem:

  • The player wins $6, that is, Ayo loses £6, if he rolls a 6 and spins a 1, hence the probability is \frac{1}{6} \times \frac{1}{12} = \frac{1}{72}.
  • The player wins $3, that is, Ayo loses £3, if he rolls a 3 on at least one of the spinner or the dice, hence, considering three cases(both and either the spinner of the dice), the probability is \frac{1}{6} \times \frac{1}{12} + \frac{1}{6} \times \frac{11}{12} + \frac{5}{6} \times \frac{1}{12} = \frac{1 + 11 + 5}{72} = \frac{17}{72}
  • In the other cases, Ayo wins £1.40, with 1 - \frac{18}{72} = \frac{54}{72} probability.

Hence, his expected profit for a single game is:

E(X) = -6\frac{1}{72} - 3\frac{17}{72} + 1.4\frac{54}{72} = \frac{-6 - 3(17) + 54(1.4)}{72} = 0.2583

For 216 games, the expected value is:

E = 216(0.2583) = 55.8

Ayo can be expected to make a profit of £55.8.

To learn more about expected value, you can take a look at brainly.com/question/24855677

6 0
2 years ago
Which point do the graphs of f and g have in common?
pickupchik [31]

The point that the graphs of f and g have in common are (1,0)

<h3>How to get the points?</h3>

The given functions are:

f(x) = log₂x

and

g(x) = log₁₀x

We know that logarithm of 1 is always zero.

This means that irrespective of the base, the y-values of both functions will be equal to 0 at x=1

Therefore the point the graphs of f and g have in common is (1,0).

Learn more about graph on:

brainly.com/question/19040584

#SPJ1

6 0
2 years ago
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