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
Ganezh [65]
2 years ago
12

You throw a ball from the balcony onto the court in the basketball arena. You release the ball at a height of 7.00 m above the c

ourt, with an initial velocity equal to 9.00 m/s at 33.0° above the horizontal. A friend of yours, standing on the court 11.0 m from the point directly beneath you, waits for a period of time after you release the ball and then begins to move directly away from you at an acceleration of 1.80 m/s2. (She can only do this for a short period of time!) If you throw the ball in a line with her, how long after you release the ball should she wait to start running directly away from you so that she’ll catch the ball exactly 1.00 m above the floor of the court?

Physics
1 answer:
Mariana [72]2 years ago
6 0

Answer:

Your friend has to wait 0.26 s after you throw the ball to start running.

Explanation:

The equation that gives the position vector of the ball is as follows:

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

Where:

x0 = initial horizontal positon

v0 = initial velocity

t = time

α = throwing angle

y0 = initial vertical position

g = acceleration due to gravity

The equation of displacement of your friend is as follows:

x = x0 + v0 · t + 1/2 · a · t²

Where:

x = position of your friend at time t

x0 = initial position

v0 = initial velocity

t = time

a = acceleration

Please, see the attached figure for a description of the situation. Notice that the frame of reference is located at the throwing point.

Let´s find the time of flight of the ball. We know that at the final time, the y-component of the vector r has to be -6.00 m (1 m above the ground). Then:

y = y0 + v0 · t ·sin α + 1/2 · g · t²

-6.00 m = 0 m + 9.00 m/s · t · sin 33.0° - 1/2 · 9.8 m/s² · t²

0 = -4.9 m/s² · t² + 9.00 m/s · sin 33.0° · t + 6.00 m

Solving the quadratic equation:

t = 1.71 s

Now that we have the time of flight, we can calculate the x-component of the vector r (the horizontal distance traveled by the ball):

x= x0 + v0 · t · cos α

x = 0m + 9.00 m/s · 1.71 s · cos 33°

x = 12.9 m

Then, your friend will have to run (12.9 m - 11.0 m) 1.9 m to catch the ball 1 m above the ground.

Let´s see, how much time it takes your friend to run that distance:

x = x0 + v0 · t + 1/2 · a · t²      (x0 = 0, v0 = 0)

x = 1/2 · a · t²

1.9 m = 1/2 · 1.80 m/s² · t²

Solving for t

t = 1.45 s

Then, since the time of flight of the ball is 1.71 s, your friend has to wait

1.71 s - 1.45 s = 0.26 s after you throw the ball to start running.

You might be interested in
A black, totally absorbing piece of cardboard of area a = 2.1 cm2 intercepts light with an intensity of 8.8 w/m2 from a camera s
PolarNik [594]

Answer:

The value of radiation pressure is 2.933 \times 10^{-8} Pa

Explanation:

Given:

Intensity I = 8.8 \frac{W}{m^{2} }

Area of piece A = 2.1 \times 10^{-4} m^{2}

From the formula of radiation pressure in terms of intensity,

   P = \frac{I}{c}

Where P = radiation pressure, c = speed of light

We know value of speed of light,

 c = 3 \times 10^{8} \frac{m}{s}

Put all values in above equation,

  P = \frac{8.8}{3 \times 10^{8} }

  P = 2.933 \times 10^{-8} Pa

Therefore, the value of radiation pressure is 2.933 \times 10^{-8} Pa

8 0
3 years ago
A bag containing 0ºC ice is much more effective in absorbing energy than one containing the same amount of 0ºC water.
rosijanka [135]

Answer:

No temperature change occurs from heat transfer if ice melts and becomes liquid water (i.e., during a phase change). For example, consider water dripping from icicles melting on a roof warmed by the Sun. Conversely, water freezes in an ice tray cooled by lower-temperature surroundings.

Explanation:

Energy is required to melt a solid because the cohesive bonds between the molecules in the solid must be broken apart such that, in the liquid, the molecules can move around at comparable kinetic energies; thus, there is no rise in temperature. Similarly, energy is needed to vaporize a liquid, because molecules in a liquid interact with each other via attractive forces. There is no temperature change until a phase change is complete. The temperature of a cup of soda initially at 0ºC stays at 0ºC until all the ice has melted. Conversely, energy is released during freezing and condensation, usually in the form of thermal energy. Work is done by cohesive forces when molecules are brought together. The corresponding energy must be given off (dissipated) to allow them to stay together Figure 2.

The energy involved in a phase change depends on two major factors: the number and strength of bonds or force pairs. The number of bonds is proportional to the number of molecules and thus to the mass of the sample. The strength of forces depends on the type of molecules. The heat Q required to change the phase of a sample of mass m is given by

Q = mLf (melting/freezing,

Q = mLv (vaporization/condensation),

where the latent heat of fusion, Lf, and latent heat of vaporization, Lv, are material constants that are determined experimentally.

6 0
2 years ago
Which statement best explains how isotopes can have different masses and still be the same element?
ss7ja [257]

Your list of choices is a very short list, and doesn't include any
correct explanation.

The mass of an atom is roughly the number of protons AND neutrons
in its nucleus, but the element only depends on how many protons are there. 

Different atoms of the same element may have different numbers of
neutrons, so their masses are different.  But they're the same element,
because they all have the same number of protons.

3 0
2 years ago
If the wind or current is pushing your boat away from the dock as you prepare to dock, which line should you secure first?
Sphinxa [80]

The line that should be secured first in pushing the boat away from the dock in preparation to dock is the bow line. When the bow line is secured, it is best to reverse it and turn to the dock, this will engage the line to tighten in a way that will help it swing back in the dock.

4 0
3 years ago
Read 2 more answers
A 42 Watt light bulb is connected to a 12 volt source of potential
abruzzese [7]

Answer:

The natural medium emanating from the Sun and other very hot sources (now recognised as electromagnetic radiation with a wavelength of 400-750 nm), within which vision is possible.

Explanation:

just the way it is

8 0
3 years ago
Other questions:
  • Two bar magnets are labeled A and B. The ends of each magnet are numbered 1 or 2, but the poles are not labeled. When A1 is brou
    6·2 answers
  • *13 POINTS* PLEASE HELP ASAP IM ON A TIME LIMIT ;-; WILL MARK BRAINLIEST what is the density of a sample that has a volume of 8c
    15·2 answers
  • Help please me please
    14·1 answer
  • Ok, so I've answered this question but I really need someone to just check through it because I have this feeling that I've done
    10·2 answers
  • Master of physics needed
    10·1 answer
  • A box with the mass of 74 kg is sitting on the ground and the bottom of the box measures 90 cm by 60 cm. What is the pressure ex
    7·1 answer
  • It takes the Earth 24 hours to make a complete rotation around its axis. 33% Part (a) What is the period of rotation of the Eart
    15·1 answer
  • Two positive point charges with charges q1 and q2 are separate by a distance of 30cm. A third positive charge qo is placed betwe
    14·1 answer
  • A roller coaster car moving at a velocity of 30 meters/second has a momentum of 2.5 _ 104 kilogram meters/second. What is its ma
    15·1 answer
  • A car travels 30 kilometers north for 2 hours, then travels 45 kilometers east for 3 hours. The car then drives south for 30 kil
    8·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!