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
antoniya [11.8K]
3 years ago
15

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

center fielder starts running and catches the ball on its way down when the ball is 0.873 m above the level at which it was hit. If the center fielder is initially 1.09 x 102 m from home plate, what must be his average speed?

Physics
1 answer:
Agata [3.3K]3 years ago
8 0

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

You might be interested in
A 6 kg box with initial speed 5 m/s slides across the floor and comes to a stop after 1.9 s. What is the coefficient of kinetic
Ilia_Sergeevich [38]

Answer:

\mu_k=0.27

Explanation:

According to the free body diagram, in this case, we have:

\sum F_x:-F_k=ma\\\sum F_y:N=mg

Recall that the force of friction is given by:

F_k=\mu_k N

Replacing and solving for the coefficient of kinetic friction:

-\mu_kN=ma\\-\mu_k(mg)=ma\\\mu_k=-\frac{a}{g}

We have an uniformly accelerated motion. Thus, the acceleration is defined as:

a=\frac{v_f-v_0}{t}\\a=\frac{0-5\frac{m}{s}}{1.9s}\\a=-2.63\frac{m}{s^2}

Finally, we calculate \mu_k:

\mu_k=-\frac{-2.63\frac{m}{s^2}}{9.8\frac{m}{s^2}}\\\mu_k=0.27

4 0
3 years ago
local AM radio station broadcasts at a frequency of 685.9 kHz. Calculate the wavelength at which they are broadcasting. Waveleng
natta225 [31]

Answer:

λ = 437 m.

Explanation:

  • Since a radio wave is a electromagnetic type of wave, it propagates approximately at the same speed of light in vacuum, 3*10⁸ m/s.
  • As in any wave, there exist a fixed relationship between the propagation speed, the wavelength and the frequency of the radio wave, as follows:

       c = \lambda* f (1)

  • Replacing by the values of the speed and the frequency, and solving for the wavelength λ, we get:

       \lambda = \frac{c}{f} =\frac{3e8 m/s}{685.9e31/s} =437 m  (2)

8 0
2 years ago
E-mail is usually a poor choice for the distribution of sensitive electronic files because
Slav-nsk [51]
D. email is saved on the server that transfers is
6 0
3 years ago
Read 2 more answers
PLEASE ANSWER FAST!!! WILL GIVE BRAINLIEST!!!!!
Alex17521 [72]
I would go with Segment D.
5 0
3 years ago
Read 2 more answers
Which of the following occurs when a covalent bond forms?
Eddi Din [679]

Your answer is...

<em>B) Electrons in valence shells are shared between nuclei.</em>

<em />

Explanation:

The simple definition of a covalent bond is a strong force when two atoms share one or more pairs of electrons.

Popular examples of covalent bonds would be:

Carbon Monoxide (CO)

Methane (CH_{4})

Water (H_{2} O)

4 0
3 years ago
Other questions:
  • A 19.3 kg dog is running northward at 2.98 m/s , while a 6.26 kg cat is running eastward at 3.64 m/s . Their 78.7 kg owner has t
    10·1 answer
  • In the example of jumping off a chair, what is the impulse that will stop your fall?
    10·1 answer
  • Parachutes utilize maximum air ____ in order to limit the acceleration of the fall.
    7·2 answers
  • Calculate the speed of a bus that travels a distance of 55 miles in 0.75 hours.
    13·1 answer
  • If an object has a volume of 2.5mL and a mass of 10g than what is the density of an object?
    7·1 answer
  • A loop with a break in it that prevents current form flowing is called a(n) blank circuit
    14·1 answer
  • All of the following activities produce quantitative data exept
    9·1 answer
  • 11 kg is a familiar weight for a bag of flour. You are baking cookies for a Save The Rain Forest fund drive. It takes 500 g of f
    6·1 answer
  • The amplitude of a wave is the height of a wave as measured from the highest point on the wave________ to the lowest point on th
    15·2 answers
  • Find the volume of a fish tank 105cm long 75cm wide and 80.5cm high using scientific notation
    8·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!