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
mrs_skeptik [129]
3 years ago
14

A major leaguer hits a baseball so that it leaves the bat at a speed of 31.3 m/s and at an angle of 36.7 ∘ above the horizontal.

You can ignore air resistance.
A) At what two times is the baseball at a height of 9.00 m above the point at which it left the bat?
t1,2 = _____ s
B) Calculate the horizontal component of the baseball's velocity at each of the two times you found in part (a).
vh1,2 = _____ m/s
C) Calculate the vertical component of the baseball's velocity at each of the two times you found in part (a).
v v1,2 = _____ m/s
D) What is the magnitude of the baseball's velocity when it returns to the level at which it left the bat?
v = ____ m/s
E) What is the direction of the baseball's velocity when it returns to the level at which it left the bat?
= ______ degrees below the horizontal
Physics
1 answer:
OLEGan [10]3 years ago
5 0

Answer:

A) t₁ = 0.56 s t₂ =3.26 s

B) vh₁=vh₂ = 25.1 m/s

C) v₁ = 13.2 m/s  v₂ = -13.2 m/s

D) v = 31. 3 m/s

E) 36.7º below horizontal.  

Explanation:

A) As the only acceleration of the baseball is due to gravity, as it is constant, we can apply the kinematic equations in order to get times.

First, we can get the horizontal and vertical components of the velocity, as the movements  along these directions are independent each other.

v₀ₓ = v* cos 36.7º = 31.3 m/s * cos 36.7º = 25.1 m/s

v₀y = v* sin 36.7º =  31.3 m/s * sin 36.7º = 18.7 m/s

As in the horizontal direction, movement is at constant speed, the time, at any point of the trajectory, is defined by the vertical direction.

We can apply to this direction the kinematic equation that relates the displacement, the initial velocity and time, as follows:

Δy = v₀y*t -1/2*g*t²

We can replace Δy, v₀y and g for the values given, solving a quadratic equation for t, as follows:

4.9*t²-18.7t + 9 = 0

The two solutions for  t, are just the two times at which the baseball is at a height of 9.00 m above the point at which it left the bat:

t = 1.91 sec +/- 1.35 sec.

⇒ t₁ = 0.56 sec   t₂= 3.26 sec.

B) As we have already told, in the horizontal direction (as gravity is always downward) the movement is along a straight path, at a constant speed, equal to the x component of the initial velocity.

⇒ vₓ = v₀ₓ = 25.1 m/s

C) In order to get the value of  the vertical components at the two times that we have just found, we can apply the definition of acceleration (g in this case), solving for vfy, as follows:

vf1 = v₀y - g*t₁ = 18.7 m/s - (9.8m/s²*0.56 sec) = 13.2 m/s

vf₂ = v₀y -g*t₂ = 18.7 m/s - (9.8 m/s²*3.26 sec) = -13.2 m/s

D) In order to get the magnitude of  the baseball's velocity when it returns to the level at which it left the bat, we need to know the value of the vertical component at this time.

We could do in different ways, but the easiest way is using the following kinematic equation:

vfy² - v₀y² = 2*g*Δh

If we take the upward path, we know that at the highest point, the baseball will come momentarily to an stop, so at this point, vfy = 0

We can solve for Δh, as follows:

Δh = v₀y² / (2*g) = (18.7m/s)² / 2*9.8 m/s² = 17.8 m

Now, we can use the same equation, for the downward part, knowing that after reaching to the highest point, the baseball will start to fall, starting from rest:

vfy² = 2*g*(-Δh) ⇒ vfy = -√2*g*Δh = -√348.9 = -18. 7 m/s

The horizontal component is the same horizontal component of the initial velocity:

vx = 25.1 m/s

We can get the magnitude of the baseball's velocity when it returns to the level at which it left the bat, just applying Pythagorean Theorem, as follows:

v = √(vx)² +(vfy)² = 31.3 m/s

E) The direction below horizontal of the velocity vector, is given by the tangent of the angle with the horizontal, that can be obtained as follows:

tg Ф = vfy/ vx = -18.7 / 25. 1 =- 0.745

⇒ Ф = tg⁻¹ (-0.745) = -36.7º

The minus sign tell us that the velocity vector is at a 36.7º angle below the horizontal.

You might be interested in
Which of the following is an example of an immiscible liquid?
Nonamiya [84]

Answer:

the answer is 1, oil and water

4 0
3 years ago
Read 2 more answers
Freddie drives his car 10 km North. He stops for gas and then drives 5 km South.
fgiga [73]

Answer:

5 km

Explanation:

displacement is the straight line distance from a particular point. since north and south are in opposite directions, it means that he has taken a u-turn

thus, 10 - 5 = 5km displacement

4 0
3 years ago
A train travels north at a speed of 50 m/s.
Gala2k [10]

The apparent velocity is B) 48 m/s north

Explanation:

Here we have a problem of relativity of velocities.

In fact, the train is travelling north at a speed of

v_t = 50 m/s

where this velocity is measured with respect to the ground.

At the same time, a passenger on the train is walking towards the rear (so, south) at a velocity of

v'=2 m/s

where this velocity is measured with respect to the train, which is in motion in the opposite direction.

Therefore, the apparent velocity of the passenger with respect to an observer standing on the ground is:

v=V_t - v' = 50 - 2 = 48 m/s

And the direction is north, since this number is positive.

Learn more about velocity:

brainly.com/question/5248528

#LearnwithBrainly

8 0
3 years ago
What is Newton's second law of motion?
Lesechka [4]
<h2><u>Q</u><u>u</u><u>e</u><u>s</u><u>t</u><u>i</u><u>o</u><u>n</u>:-</h2>

What is Newton's second law of motion?

<h2><u>A</u><u>n</u><u>s</u><u>w</u><u>e</u><u>r</u>:-</h2>

Newton's second law of motion states that the rate of change of momentum is directly proportional to the applied force and the direction of change of momentum takes place towards direction of applied force.

<h3>\bulletWhat do you come to know from Newton's second law of motion?</h3>

1. Concept of Momentum.

2. Measurement of Force.

_____________________________________

<h3 /><h3 /><h3 /><h3>\bf Hope \: it \: helps \: you .</h3>
7 0
3 years ago
Read 2 more answers
Which one of the following scenarios accurately describes a condition in which resonance can occur?
Readme [11.4K]
<span>Hello,

The answer is:

A vibrating tuning fork is struck and begins to vibrate as the object used to strike it is placed away from the tuning fork.</span>
7 0
3 years ago
Other questions:
  • What is the G.P.E of 675 newtons on 26000 meter mountain
    11·1 answer
  • The smallest angle of inclined desk at which a book begins to slide off the desk is 15∘ relative to the horizontal.
    6·2 answers
  • In the United States, most of our energy comes from this non-renewable resource, which has a negative effect on the environment.
    11·2 answers
  • Question 1
    10·2 answers
  • Wonder Woman and Superman fly to an altitude of 1690 km , carrying between them a chest full of jewels that they intend to put i
    10·1 answer
  • Which of the following statements is true?
    9·2 answers
  • A conductor carrying 14.7 amps of current is directed along the positive x-axis and perpendicular to a uniform magnetic field. A
    13·1 answer
  • 2 t of ferrous scrap at a temperature of 20 degrees is heated to the melting point and melted. How much to consume?
    14·1 answer
  • As fuel is burned in an electrical generator, the chemical energy of the fuel is converted into thermal energy that is used to b
    5·1 answer
  • If there were no dark energy in the universe, the value of __________ would solely determine the evolution and fate of the unive
    7·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!