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
Hello :) how to do this qn?
Finger [1]
The answer is B because oil = blockage of air and it pressures the water to be density of 0.90
3 0
2 years ago
Read 2 more answers
object is placed 15cm in front of a plane mirror. If the mirror is moved further 5cm away from the object and the image is​
solong [7]

Answer:

The image will most likely be 20cm in front the mirror since the mirror was placed further 5cm.

4 0
2 years ago
Read 2 more answers
A waterbed has a force of 1300N on the floor. It exerts 347 Pa of pressure. What is the area of the waterbed?
Sergio [31]

Answer:

Pressure = Force/Area

347 = 1300/Area

Area = 1300/347

area= 3.47m2

6 0
3 years ago
Read 2 more answers
Does gravity cause physical weathering or chemical weathering
Kazeer [188]
I think it causes physical weathering
3 0
2 years ago
What is tarzan's speed vf just before he reaches jane? express your answer in meters per second to two significant figures?
e-lub [12.9K]
Before swinging, T has only potential energy, (no speed)
Ui = mgh
Where h is the vertical displacement of T
From the laws of geometry,
cos45 = (L-h)/L
cos45 = 1-h/L
h/L = 1-cos45
h = L(1-cos45)

Therefore
Ui = mgL(1-cos45)

Proceeding the same way,
Twill raise to aheight of h' due to swing
h' = L(1-cos30)
The PE of T after swing is
Uf = mgh'
Uf = mgL(1-cos30)

Along with the PE , T has some kinetic energy results due to the moment.
Tf = 0.5*mv^2

According to the law of conservation of energy,
Ui = Uf+Tf
mgL(1-cos45) = mgL(1-cos30) + 0.5*mv^2
gL(co30-cos45) = 0.5*v^2
9.8*20*(co30-cos45) = 0.5*V^2
v = 7.89 m/s

<span>The speed f T after swing is 7.89 m/s</span>
3 0
3 years ago
Other questions:
  • A +4.0- μC charge is placed on the x axis at x = +3.0 m, and a −2.0- μC charge is located on the y axis at y = −1.0 m. Point A i
    9·1 answer
  • If two firecrackers produce a sound level of 81 dBdB when fired simultaneously at a certain place, what will be the sound level
    7·1 answer
  • A sailboat is moving across the water at 3.0 m/s. A gust of wind fills its sails and it accelerates at a constant 2.0 m/s2. At t
    12·1 answer
  • To calculate the change in kinetic energy, you must know the force as a function of _______. The work done by the force causes t
    11·1 answer
  • Un auto de 1000 kg que lleva una velocidad de 72 km/h se detiene en una distancia de 100 metros cuando se le aplican los frenos.
    9·1 answer
  • (marking brainliest) pease help asap! both of the questions are in the pdf, and please let me know which is question one and whi
    12·1 answer
  • How much heat is needed to raise the temperature of 50.0 g of water by 25.0°C
    9·2 answers
  • PLEASE HELP WITH THESE WILL GIVE BRAINLEIST
    10·2 answers
  • How far is a light year?? ​
    6·2 answers
  • Please help me I’ll mark you Brainly!!<br> QUICK
    7·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!