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
Setler [38]
2 years ago
15

A batter hits a ball and it is caught 4 seconds later 100 m from home plate. What is the initial velocity (vector!!!) of the bal

l?(Note: the ball is hit and caught at the same distance from the ground.
Physics
1 answer:
Eddi Din [679]2 years ago
4 0

Answer:

The initial velocity vector of the ball is;

\underset{u}{\rightarrow} = 25·i + 19.6·j

Explanation:

The given parameters are;

The time of flight of the ball = 4 seconds

The horizontal distance from the plate at which the ball is caught = 100 m

Let 'u', represent the initial velocity, we have;

u × cos(θ) × t = u × cos(θ) × 4 s = 100 m

u × cos(θ) = 25 m/s...(1)

t = \dfrac{2 \cdot u \cdot sin(\theta)}{g} = \dfrac{2 \cdot u \cdot sin(\theta)}{9.8 \ m/s^2} = 4 \ seconds

∴ 2·u·sin(θ) = 9.8 m/s² × 4 s = 39.2 m/s

\therefore \dfrac{2 \cdot u \cdot sin(\theta)}{u \cdot cos(\theta)} = 2 \cdot tan(\theta) = \dfrac{39.2 \ m/s}{25 \  m/s} = 1.568

tan(θ) = 1.568/2 = 0.784

θ = arctan(0.784) ≈ 38.096°

The direction of the velocity  vector of the ball, θ ≈ 38.096°

From equation (1), we have;

u × cos(θ) = 25 m/s

∴ u = 25 m/s/cos(θ) = 25 m/s/cos(arctan(0.784)) = 31.7672787629 m/s

The magnitude of the initial velocity vector, u = 31.7672787629 m/s

The vertical component of the initial velocity, u_y = u × sin(θ)

∴ u_y = 31.7672787629 × sin(arctan(0.784))

Therefore, the initial velocity vector of the ball is approximately, v = 31.767 m/s in a direction 38.096° above the horizontal, from which we have;

u = uₓ·i + u_y·j = 25·i + 19.6·j

\underset{u}{\rightarrow} = 25·i + 19.6·j

You might be interested in
Charge g is distributed in a spherically symmetric ball of radius a. (a) Evaluate the average volume charge density p. (b) Now a
nasty-shy [4]

Answer:

Explanation:

The volume of a sphere is:

V = 4/3 * π * a^3

The volume charge density would then be:

p = Q/V

p = 3*Q/(4 * π * a^3)

If the charge density depends on the radius:

p = f(r) = k * r

I integrate the charge density in spherical coordinates. The charge density integrated in the whole volume is equal to total charge.

Q = \int\limits^{2*\pi}_0\int\limits^\pi_0  \int\limits^r_0 {k * r} \, dr * r*d\theta* r*d\phi

Q = k *\int\limits^{2*\pi}_0\int\limits^\pi_0  \int\limits^r_0 {r^3} \, dr * d\theta* d\phi

Q = k *\int\limits^{2*\pi}_0\int\limits^\pi_0 {\frac{r^4}{4}} \, d\theta* d\phi

Q = k *\int\limits^{2*\pi}_0 {\frac{\pi r^4}{4}} \,  d\phi

Q = \frac{\pi^2 r^4}{2}}

Since p = k*r

Q = p*π^2*r^3 / 2

Then:

p(r) = 2*Q / (π^2*r^3)

3 0
2 years ago
How far will you travel if you walk for 50 seconds at 8 m/s?
Rom4ik [11]

Answer:

تتتتتتتتتتتتتتتت

Explanation:

7 0
3 years ago
Read 2 more answers
What do we get from the area between the speed-time graph of a body and the time axis?​
maxonik [38]

Explanation:

The area between the speed-time graph f a body and time axis measures the distance travelled by the body

7 0
2 years ago
Describing Energy Transformations
UNO [17]

Answer:

chemical energy to electrical energy to sound energy to heat energy

4 0
3 years ago
The index of refraction of a substance is 1.5. Find the sine of the angle of refraction if the sine of the angle of incidence is
Mariulka [41]
We can answer the problem by Snell's Law:

Snell's law<span> (also known as </span>Snell<span>–Descartes </span>law<span> and the </span>law<span> of refraction) is a formula used to describe the relationship between the angles of incidence and refraction, when referring to light or other waves passing through a boundary between two different isotropic media, such as water, glass, or air.</span>
7 0
2 years ago
Other questions:
  • A bullet with a mass ????b=13.5mb=13.5 g is fired into a block of wood at velocity ????b=253vb=253 m/s. The block is attached to
    7·1 answer
  • A test rocket is launched vertically from ground level (y = 0 m), at time t = 0.0 s. The rocket engine provides constant upward
    6·1 answer
  • Increasing the amount of current that flows through a wire ______ the strength of an electromagnet
    12·2 answers
  • How does the law of conservation of mass apply to this reaction: C2H4 + O2 → H2O + CO2?
    7·2 answers
  • What conventions are used in SI to indicate units
    9·1 answer
  • Can anyone provide me the answer with explanation?​
    8·2 answers
  • An airplane flies 58 miles in 5 minutes. What is its average speed in miles per hour?
    11·2 answers
  • What would the charge be on an ion with 8 protons 7 neutrons and 6 elements?
    11·1 answer
  • The particle in the atom with a negative charge is the ______<br> Answer here
    13·2 answers
  • Initial velocity 10 m/s accelerates at 5 m/s for 2 seconds whats the final velocity
    12·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!