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
Ne4ueva [31]
3 years ago
15

A ball is dropped from rest from the top of a building of height h. At the same instant, a second ball is projected vertically u

pward from ground level, such that it has zero speed when it reaches the top of the building.
(a) When do the two balls pass each other?
(b) Which ball has greater speed when they are passing?
(c) What is the height of the two balls when they are passing?
Physics
1 answer:
uranmaximum [27]3 years ago
7 0

Answer:

a) t = \sqrt{\frac{h}{2g}}

b) Ball 1 has a greater speed than ball 2 when they are passing.

c) The height is the same for both balls = 3h/4.

Explanation:

a) We can find the time when the two balls meet by equating the distances as follows:

y = y_{0_{1}} + v_{0_{1}}t - \frac{1}{2}gt^{2}  

Where:

y_{0_{1}}: is the initial height = h

v_{0_{1}}: is the initial speed of ball 1 = 0 (it is dropped from rest)

y = h - \frac{1}{2}gt^{2}     (1)

Now, for ball 2 we have:

y = y_{0_{2}} + v_{0_{2}}t - \frac{1}{2}gt^{2}    

Where:

y_{0_{2}}: is the initial height of ball 2 = 0

y = v_{0_{2}}t - \frac{1}{2}gt^{2}    (2)

By equating equation (1) and (2) we have:

h - \frac{1}{2}gt^{2} = v_{0_{2}}t - \frac{1}{2}gt^{2}

t=\frac{h}{v_{0_{2}}}

Where the initial velocity of the ball 2 is:

v_{f_{2}}^{2} = v_{0_{2}}^{2} - 2gh

Since v_{f_{2}}^{2} = 0 at the maximum height (h):

v_{0_{2}} = \sqrt{2gh}

Hence, the time when they pass each other is:

t = \frac{h}{\sqrt{2gh}} = \sqrt{\frac{h}{2g}}

b) When they are passing the speed of each one is:

For ball 1:

v_{f_{1}} = - gt = -g*\sqrt{\frac{h}{2g}} = - 0.71\sqrt{gh}

The minus sign is because ball 1 is going down.

For ball 2:

v_{f_{2}} = v_{0_{2}} - gt = \sqrt{2gh} - g*\sqrt{\frac{h}{2g}} = (\sqrt{1} - \frac{1}{\sqrt{2}})*\sqrt{gh} = 0.41\sqrt{gh}

Therefore, taking the magnitude of ball 1 we can see that it has a greater speed than ball 2 when they are passing.

c) The height of the ball is:

For ball 1:

y_{1} = h - \frac{1}{2}gt^{2} = h - \frac{1}{2}g(\sqrt{\frac{h}{2g}})^{2} = \frac{3}{4}h

For ball 2:

y_{2} = v_{0_{2}}t - \frac{1}{2}gt^{2} = \sqrt{2gh}*\sqrt{\frac{h}{2g}} - \frac{1}{2}g(\sqrt{\frac{h}{2g}})^{2} = \frac{3}{4}h

Then, when they are passing the height is the same for both = 3h/4.

I hope it helps you!                  

You might be interested in
A runner runs 2.0 km in 5.0 minutes
Nadya [2.5K]

Answer: What is this supposed to be converted into?

Explanation:

4 0
2 years ago
Read 2 more answers
Si un ciclista se mueve a una velocidad de 5 m/s y acelera 1 m/s2, a los 10 segundos su velocidad será
MrRa [10]

Answer:

A los 10 segundos su velocidad será 15 \frac{m}{s}

Explanation:

La aceleración de un objeto es una magnitud que indica cómo cambia la velocidad del objeto en una unidad de tiempo.

En otras palabras, la aceleración relaciona los cambios de la velocidad con el tiempo en el que se producen, es decir que mide cómo de rápidos son los cambios de velocidad:

  • Una aceleración grande significa que la velocidad cambia rápidamente.
  • Una aceleración pequeña significa que la velocidad cambia lentamente.
  • Una aceleración cero significa que la velocidad no cambia.

La aceleración "a" puede ser calculada mediante la expresión:

a=\frac{vfinal - vinicial}{tiempo}

En este caso:

  • a= 1 \frac{m}{s^{2} }
  • vfinal= ?
  • vinicial= 5 \frac{m}{s}
  • tiempo= 10 s

Reemplazando:

1\frac{m}{s^{2} }=\frac{vfinal - 5\frac{m}{s} }{10 s}

Resolviendo se obtiene:

1 \frac{m}{s^{2} } *10 s= vfinal - 5 \frac{m}{s}

10 \frac{m}{s} = vfinal - 5 \frac{m}{s}

10 \frac{m}{s} + 5 \frac{m}{s} = vfinal

15 \frac{m}{s} = vfinal

<u><em>A los 10 segundos su velocidad será 15 </em></u>\frac{m}{s}<u><em></em></u>

5 0
2 years ago
A hot ball of gas in outer space that creates its own energy is called a _____.
Fynjy0 [20]
It's called a star when it creates its own energy
3 0
3 years ago
Apply the law of conservation of energy and describe the energy transformations that occur as you coast down a long hill on a bi
m_a_m_a [10]
As you coast down a long hill on your bicycle, potential energy from your height is converted to kinetic energy as you and your bike are pulled downward by gravity along the slope of the hill. While there is air resistance and friction slowing you down by a little bit, your speed increases gradually until you apply the brakes, causing enough friction to slow yourself and the bike to a stop at the bottom.

A roller coaster will have higher kinetic energy at the lower hill because it will have already been moving as opposed to the initial hill. But I'm not one hundred percent certain. You can always google this stuff, but I do know for sure that at the first hill, the roller coaster will have higher potential energy.
Hope this helps!
4 0
3 years ago
Wich type of mutation occurs in reproductive cell and can be passed to offspring? A sommatic mutation B germline mutation C poin
ryzh [129]

The answer to your question is,

B. Germline mutation

-Mabel <3

7 0
3 years ago
Other questions:
  • The picture below shows the weather station model at a particular location.
    10·1 answer
  • A pitcher throws a 0.14-kg baseball toward the batter so that it crosses home plate horizontally and has a speed of 42 m/s just
    9·1 answer
  • Quanto vale a resultante de duas forças de mesmo módulo mesma direção e sentidos opostos atuando sobre um corpo de massa igual a
    12·2 answers
  • Which of the following should not be held constant during this experiment?
    9·2 answers
  • The tent meteorite, found in 1897 near cape York, on the west coast of Greenland, is the largest meteorite exhibited by any muse
    8·1 answer
  • When electric current is flowing in a metal, the electrons are movinga. at nearly the speed of light.b. at the speed of sound in
    5·1 answer
  • What causes a rolling object
    13·1 answer
  • A ball is thrown off a cliff at a speed of 10 m/s in a horizontally direction. The ball reaches the ground 1.5 seconds. If the b
    5·1 answer
  • Photosynthesis uses all of the following except _____ to make food.
    8·2 answers
  • What speed should a satellite of mass 4,900 kg moving around
    9·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!