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
Kazeer [188]
3 years ago
14

Baseball player swings and hits a pop fly straight up in the air to the catcher. the height of the baseball in meters t seconds

after it is hit is given by the quadratic function h left parenthesis t right parenthesis equals negative 4.9 t squared plus 34.3 t plus 1h(t)=â4.9t2+34.3t+1. how long does it take for the baseball to reach its maximumâ height? what is the maximum height obtained by theâ baseball?
Physics
1 answer:
andre [41]3 years ago
4 0
The height at time t is given by
h(t) = -4.91t² + 34.3t + 1

When the ball reaches maximum height, its derivative, h'(t) = 0.
That is,
-2(4.91)t+34.3 = 0
-9.82t + 34.3 = 0
t = 3.4929 s

Note that h''(t) = -9.82 (negative) which confirms that h will be maximum.

The maximum height is
hmax = -4.91(3.4929)² + 34.3(3.4929) + 1
          = 60.903 m

Answer:
The ball attains maximum height in 3.5 s (nearest tenth).
The ball attains a maximum height of 60.9 m (nearest tenth)

You might be interested in
A simple generator is used to generate a peak output voltage of 25.0 V . The square armature consists of windings that are 7.0 c
4vir4ik [10]

Answer:

<h3>The 28 loops wound on the square armature</h3>

Explanation:

Peak output voltage \epsilon _{peak}  = 25 V

Area of square armature A = (7 \times 10^{-2} )^{2}  = 49 \times 10^{-4}

Magnetic field B = 0.490 T

Angular frequency \omega = 2\pi f = 2 \pi \times 60 = 120\pi

According to the law of electromagnetic induction,

     \epsilon _{peak} = NBA \omega

Where N = number of loops of wire.

  N = \frac{25}{49 \times 10^{-4} \times 0.49 \times 120\pi  }

  N = 27.6 ≅ 28

Thus, 28 loops of wire should be wound on the square armature.

6 0
3 years ago
1. A car is traveling at 36 m/s hits a tree and comes to rest in 0.05 seconds.
QveST [7]

Answer: a. -720m/s^2

b. Yes, airbags will deploy

Explanation:

The formula for acceleration is:

= (Final velocity - Initial velocity)/Time

Final velocity = 0m/s

Initial velocity = 36m/s

Time taken = 0.05s

= (Final velocity - Initial velocity)/Time

= (0 - 36)/0.05

= -36/0.05

= -720m/s^2.

Since it's negative, it shows that there was a deceleration.

2. Yes the airbag will deploy since the acceleration gotten is more than -600 m/s^2.

3 0
3 years ago
State one of Kepler's laws of gravitation
jekas [21]
All planets move around the sun
3 0
3 years ago
Read 2 more answers
baseball is hit into the air at an initial speed of 37.2 m/s and an angle of 49.3 ° above the horizontal. At the same time, the
Agata [3.3K]

Answer:

The average speed of the fielder is 5.24 m/s

Explanation:

The position vector of the ball after it was hit can be calculated using the following equation:

r = (x0 + v0 · t · cos α, y0 + v0 · t · sin α + 1/2 · g · t²)

Where:

r = position vector at time t.

x0 = initial horizontal position.

v0 = initial velocity.

t = time.

α = launching angle.

y0 = initial vertical position

g = acceleration due to gravity (-9.8 m/s² considering the upward direction as positive).

Please, see the attached figure for a graphical description of the problem.

When the ball is caught, its position vector will be (see r1 in the figure):

r1 = (r1x, 0.873 m)

Then, using the equation of the position vector written above:

r1x = x0 + v0 · t · cos α

0.873 m = y0 + v0 · t · sin α + 1/2 · g · t²

Since the frame of reference is located at the point where the ball was hit, x0 and y0 = 0. Then:

r1x = v0 · t · cos α

0.873 m = v0 · t · sin α + 1/2 · g · t²

Let´s use the equation of the y-component of r1 to obtain the time of flight of the ball:

0.873 m = 37.2 m/s · t · sin 49.3° - 1/2 · 9.8 m/s² · t²

0 = -0.873 m + 37.2 m/s · t · sin 49.3° - 4.9 m/s² · t²

Solving the quadratic equation:

t = 0.03 s and t = 5.72 s.

It would be impossible to catch the ball immediately after it is hit at t = 0.03 s. Besides, the problem says that the ball was caught on its way down. Then, the time of flight of the ball is 5.72 s.

With this time, we can calculate r1x which is the horizontal distance traveled by the ball from home:

r1x = v0 · t · cos α

r1x = 37.2 m/s · 5.72 s · cos 49.3°

r1x = 1.39 × 10² m

The distance traveled by the fielder is (1.39 × 10² m - 1.09 × 10² m) 30.0 m.

The average velocity is calculated as the traveled distance over time, then:

average velocity = treveled distance / elapsed time

average velocity = 30.0 m / 5.72 s = 5.24 m/s

8 0
3 years ago
Describe asexual reproduction
Brrunno [24]
“Asexual reproduction is a type of reproduction by which offspring arise from a single organism, and inherit the genes of that parent only; it does not involve the fusion of gametes, and almost never changes the number of chromosomes.” -Wikipedia
4 0
3 years ago
Other questions:
  • How does the mass of an object affect its inertia?
    7·1 answer
  • Bandwidth is the: Select one: A. number of frequencies that can be broadcast through a medium. B. number of cycles per second th
    8·1 answer
  • You watch a distant lady driving nails into her front porch at a regular rate of 2 strokes per second. You hear the sound of the
    13·1 answer
  • Material speed of light
    10·1 answer
  • A box weighing 103 kg and a football weigh 0.41 and they dropped at the same time the top of a 98 m tall building.
    13·1 answer
  • No work is done when a person is standing by caring a load of 25kg for one hour why​
    10·1 answer
  • To test the strength of a retainment wall designed to protect a nuclear reactor,
    14·1 answer
  • 5
    9·2 answers
  • Why this app says im in high school.?. im in middle and im 13
    7·1 answer
  • Think of an animal that has a distinctive or unusual body shapes. Describe how its body shape helps its momentum and how momentu
    12·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!