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
podryga [215]
3 years ago
6

A billiard ball is dropped from a height of 64 feet. Use the position function s(t) = –16???? 2 + ????0???? + ????0 to answer th

e following. a. Determine the position function s(t), the velocity function v(t), and the acceleration function a(t). b. What is the velocity of the ball at impact?
Physics
1 answer:
Delicious77 [7]3 years ago
6 0

Answer:

s(t) = -16*t^2 + 64

v(t) = -32*t

a(t) = -32 ft/s^2

v(t) = 64 ft/s ... At impact

Explanation:

Given:-

- The height of the billiard ball t = 0 , h = 64 ft.

- The position function of an object under gravity is given by:

                                    s(t) = -16*t^2 + v_o*t + s_o

Find:-

a. Determine the position function s(t),

b. the velocity function v(t),

c. the acceleration function a(t).

d. What is the velocity of the ball at impact?

Solution:-

- To determine the position function we must initialize our problem and use the given general equation.

- s(t) is the position of the billiard ball from the ground at time t. So when t = 0, then s(t) = h. Hence, we have:

                                  s(t) = s_o = h = 64 ft

- Similarly we know that v_o is the initial velocity of the ball. Since, the ball was dropped we say that the initial velocity v_o = 0. Hence, the position of the ball from ground is given by following expression:

                                  s(t) = -16*t^2 + 64  

- To find the velocity expression v(t) we will take the time derivative of the position expression s(t) as follows:

                                  v(t) = d s(t) / dt

                                  v(t) = -16*2*t + 0

                                  v(t) = -32*t ft/s

- Similarly, the expression for acceleration a(t) is given by the time derivative of the velocity expression v(t) as follows:

                                  a(t) = d v(t) / dt

                                  a(t) = -32*t

                                  a(t) = -32 ft/s^2

- The velocity of ball at impact can be determined by evaluating s(t) = 0 and find the value for time t. Then that time t can be substituted in the velocity expression v(t) for final velocity. Or we could use the following 3rd kinematic equation as follows:

                                 v(t)^2 - 0^2 = 2*a(t)*s_o

                                 v(t)^2 = 2*(32)*(64)

                                 v(t) = 64 ft/s

- The ball has a velocity of 64 ft/s at impact!

You might be interested in
During a medical evaluation, the doctor can __________.
WINSTONCH [101]
<span>During a medical evaluation, the doctor can D. all of the above. It is the doctor's duty to do all of these things - to establish some guidelines for activities, to see whether these programs are appropriate for the person in question, and to help them pick activities that will be safe for them and which they will be able to do without harming their bodies. These are all the things that doctors do in order to help their patients lead a safe and healthy life.</span>
3 0
3 years ago
Read 2 more answers
Which is a standard unit of measurement​
ruslelena [56]
There are some more like Time - second (s)
Amount of substance - mole (mole)
Electric current - ampere (A)
Temperature - kelvin (K)
Luminous intensity - candela (cd)

6 0
2 years ago
A piece of transparent material that is used to focus light and form a image
Soloha48 [4]

Convex Lenses are used to focus light and form a image. They are transparent.

They are one type of lenses. Different type of lenses are used to focus light differently. The basic lenses are concave and convex. Convex lenses converge light falling on it whereas concave lenses diverge light falling on it.

4 0
3 years ago
Read 2 more answers
One property that makes electromagnetic waves differ from other types of waves is that they can
IgorC [24]
Electromagnectic Waves Travel In A Vacuum
4 0
3 years ago
Read 2 more answers
4. show your understanding of electric and magnetic forces<br> below.
Vitek1552 [10]

Answer:

Explanation:

Electric forces exist among stationary electric charges; both electric and magnetic forces exist among moving electric charges. ... The magnetic force between two moving charges may be described as the effect exerted upon either charge by a magnetic field created by the other.

8 0
2 years ago
Other questions:
  • Light refracts when traveling from air into glass because light
    8·1 answer
  • An apple is pushed across a table with a velocity of 3.74 m/s rolls too far and falls 0.89
    6·1 answer
  • a 100gm copper block is heated in boiling water for 10min and then it is dropped into 150gm of water at 30 C in a 200gm calorime
    10·1 answer
  • Assume that charge −q is placed on the top plate, and +q is placed on the bottom plate of a parallel plate capacitor. What is th
    11·1 answer
  • Which one of the following terms is used to describe the bending of waves and subsequent spreading around obstacles or the edges
    8·1 answer
  • A triangle with equal sides of length 14 cm has -2.5-nC charged objects at each corner. Determine the direction of the electrica
    15·1 answer
  • A cat with a mass of 4.50 kilograms sits on a ledge 0.800 meters above the ground. What is the potential energy of the cat? 346
    5·2 answers
  • Which object moves in simple harmonic motion?\
    8·1 answer
  • Within which type of system is the total energy conserved?
    14·1 answer
  • Explain why energy from the sun cannot reach us by conduction or convection?
    5·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!