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
Molodets [167]
3 years ago
7

Chris shoots an arrow up into the air. The height of the arrow is given by the function h(t) = - 16t2 + 64t + 23 where t is the

time in seconds. What is the maximum height of the arrow?
Physics
2 answers:
Ghella [55]3 years ago
7 0

Completing the square gives the answer right away.

-16t^2+64t+23=-16(t^2-4t)+23=-16(t^2-4t+4-4)+23=-16((t-2)^2-4)+23

\implies h(t)=-16(t-2)^2+87

which indicates a maximum height of 87 when t=2.

vagabundo [1.1K]3 years ago
6 0

Answer:

The maximum height of the arrow is 87 meters.

Explanation:

If we look at the height function of the arrow

                h(t)=-16t^{2} +64t+23

we see that its a parabola whose principal coefficient is negative, that means is inverted or upside down.

When the arrow reaches maximum height its velocity will be zero. The velocity of an object is the derivative of the position function, in this case the so called height function.

So we we derivate the height function to get that

                h'(t)=-32t+64

we must find the t that makes this equation equal to zero:

                -32t+64=0

                          32t=64

                             t=2s

we replace this value of t in the height function:

                h(2 s)=-16.(2s)^{2} +64.(2s)+23

we get that

                 h(2s)=87m

The maximum height of the arrow is 87 meters.

We have used the MKS system which uses the meter, kilogram and second as base units.

You might be interested in
An object of mass 8kg is attached to massless string of length 2m and swum with a tangential velocity of 3 what is the tension o
Paul [167]

Answer:

36 N

Explanation:

If the object of mass, m = 8 kg is swung in a horizontal circle of radius, r = 2m = length of string with tangential velocity v = 3 m/s, the tension in the string is the centripetal force which is T = mv²/r

= 8 kg × (3 m/s)²/2 m

= 4 kg × 9 m/s²

= 36 N

6 0
3 years ago
Which force requires contact
jekas [21]
Gravity?????????? or maybe like any object
5 0
3 years ago
Read 2 more answers
g You drop a 3.6-kg ball from a height of 3.5 m above one end of a uniform bar that pivots at its center. The bar has mass 9.9 k
Salsk061 [2.6K]

Answer:

h = 3.5 m

Explanation:

First, we will calculate the final speed of the ball when it collides with a seesaw. Using the third equation of motion:

2gh = v_f^2 - v_i^2\\

where,

g = acceleration due to gravity = 9.81 m/s²

h = height = 3.5 m

vf = final speed = ?

vi = initial speed = 0 m/s

Therefore,

(2)(9.81\ m/s^2)(3.5\ m) = v_f^2 - (0\ m/s)^2\\v_f = \sqrt{68.67\ m^2/s^2}\\v_f = 8.3\ m/s

Now, we will apply the law of conservation of momentum:

m_1v_1 = m_2v_2

where,

m₁ = mass of colliding ball = 3.6 kg

m₂ = mass of ball on the other end = 3.6 kg

v₁ = vf = final velocity of ball while collision = 8.3 m/s

v₂ = vi = initial velocity of other end ball = ?

Therefore,

(3.6\ kg)(8.3\ m/s)=(3.6\ kg)(v_i)\\v_i = 8.3\ m/s

Now, we again use the third equation of motion for the upward motion of the ball:

2gh = v_f^2 - v_i^2\\

where,

g = acceleration due to gravity = -9.81 m/s² (negative for upward motion)

h = height = ?

vf = final speed = 0 m/s

vi = initial speed = 8.3 m/s

Therefore,

(2)(9.81\ m/s^2)h = (0\ m/s)^2-(8.3\ m/s)^2\\

<u>h = 3.5 m</u>

6 0
2 years ago
Estimate the moment of inertia of a bicycle wheel 66 cm in diameter. The rim and tire have a combined mass of 1.2 Kg
Fed [463]
<span>For a point mass the moment of inertia is just the mass times the square of perpendicular distance to the rotation axis, I = mr^2. That point mass relationship becomes the basis for all other moments of inertia since any object can be built up from a collection of point masses. So the I = (1.2 kg)(0.66m/2)^2 = 0.1307 kg m2</span>
3 0
3 years ago
Cmon Guys help your pal abigail
NemiM [27]
13-16 that is where they’re located at
8 0
3 years ago
Other questions:
  • PERSONAL QUESTION <br> if a bird can fly why can't a fly just bird ?​
    11·2 answers
  • Which of these correctly describes whether a girl holding a ball in the same position is doing work on the ball?
    14·1 answer
  • Which pair of labels is correct? A: Maximum kinetic energy C: Maximum gravitational potential energy B: Maximum kinetic energy D
    9·2 answers
  • (b) The cabin and passengers have a total mass of 800 kg. The vertical distance between
    12·1 answer
  • What is one characteristic of the organization of the Periodic Table?
    12·1 answer
  • A microscope using ultraviolet light is used to study bacteria. If the aperture diameter is 1.5 cm and it is desired to distingu
    12·1 answer
  • Question 10 (1 point)
    5·1 answer
  • BERE
    7·2 answers
  • . The penalties for a person's second DUI conviction include completion of __________ hours of DUI school.
    13·1 answer
  • Find the speed of a satellite in a circular orbit around the Earth with a radius 3.57 times the mean radius of the Earth. (Radiu
    5·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!