Answer:
a) 1.38 s
b) v₀ = 3.92 m/s θ₀ = 53.1º
c) vf = 10.7 m/s θf = -77.2º
Explanation:
a)
Once the diver leaves the board, she has an initial velocity vector, that we can split in two directions perpendicular each other, the vertical direction (coincident with the y-axis, positive upward) and the horizontal direction (coincident with the x-axis, positive away from the diving board).These velocities, are independent each other, due to they are perpendicular.In the horizontal direction, since no acceleration takes place, she keeps the horizontal component v₀ₓ, constant.In the vertical direction, she is always accelerated downward by gravity, which constant value is g = 9.8m/s2.With this all information, we can find the total time since she left the diving board till she strikes the water below, taking advantage of the fact that she reached to a maximum height of 5.5 m,i.e. , 0.5m above the diving board. When at this point, the vertical component of the velocity is zero, so we can write the following kinematic equation:[tex]v_{fy} ^{2} - v_{oy} ^{2} = 2* g* \Delta y (1)[/tex]
Solving for v₀y in (1):[tex]v_{oy} = \sqrt{2*g*\Delta_{ymax} } = \sqrt{2*9.8m/s2*0.5m} = 3.13 m/s (2)[/tex]
When she is at the highest point, her final vertical speed is zero, so we can find the time when she reached to this point, applying the definition of acceleration, as follows:[tex]v_{fyhmax} = v_{oy} - g*t_{hmax} = 0 (3)[/tex]
Solving for t in (3), we get:[tex]t_{hmax} =- \frac{v_{oy}}{g} =\frac{3.13m/s}{9.8m/s2} = 0.32 s (4)[/tex]
Since at this point, the vertical speed is zero, we can apply the equation for the displacement (vertical in this case) for a total displacement of 5.5 m (taking as the origin the point just below the end of the diving board, on the surface of the water), with initial speed equal to zero, as follows:[tex]\Delta y = \frac{1}{2}* g * t^{2} = 5.5 m (5)[/tex]
Solving for t (which we will call t₂) in (5), we get:[tex]t_{2} = \sqrt{\frac{2*\Delta y}{g}} = \sqrt{\frac{2*5.5m}{9.8m/s2} } = 1.06 s (6)[/tex]
The total time will be just the sum of (4) (since leaving the diving board till reaching the maximum height) and (6) (from there until she strikes the water), as follows:Δt = thmax + t₂ = 0.32 s + 1.06 s = 1.38 s (7)b)
In order to know the value of v₀, we need first to get the values of vox and voy.We know that the horizontal speed remains constant, so, if we know the total time traveled (same as in a)) and the horizontal distance (given), we can find v₀ₓ applying the definition of average velocity, as follows:[tex]v_{ox} =\frac{\Delta x}{\Delta t} =\frac{3.25m}{1.38s} = 2.36 m/s (8)[/tex]
We know the value of v₀y from (2):[tex]v_{oy} = 3.13 m/s (9)[/tex]
Applying the Pythagorean theorem, we can get the magnitude of v₀ as follows:[tex]v_{o} = \sqrt{v_{ox}^{2} + v_{oy}^{2}} = \sqrt{(2.36m/s)^{2} + (3.13m/s)^{2}} = 3.92m/s (10)[/tex]
We can find the angle that it makes with the horizontal, applying the definition of tangent of an angle, as follows:[tex]tg_{(\theta o)} = \frac{v_{oy}}{v_{ox} } = \frac{3.13}{2.36} = 1.33 (11)[/tex]
⇒ θ₀ = tg⁻¹ (1.33) = 53.1º
c)
In order to find the vertical component of the final velocity, we can use the following kinematic equation, for the total vertical displacement of 5.5 m since it started to fall after reaching to the maximum speed:[tex]v_{fy} ^{2} - v_{oy} ^{2} = 2* g* \Delta y (12)[/tex]
When it started to fall, in the vertical direction, the diver was at rest, so in (12) we have v₀y = 0.Solving for vfy in (12) we get:[tex]v_{fy} = \sqrt{2*g*\Delta_{y} } = \sqrt{2*9.8m/s2*5.5m} = -10.4 m/s (13)[/tex]
We already know that the horizontal component is the same as the initial v₀ₓ, so we can find the magnitude of the final velocity applying the Pythagorean Theorem as follows:[tex]v_{f} = \sqrt{v_{fx}^{2} + v_{fy}^{2}} = \sqrt{(2.36m/s)^{2} + (-10.4m/s)^{2}} = 10.7 m/s (14)[/tex]
Finally, as we did in (11) to find the angle that it makes with the horizontal, we can find θf as follows:[tex]tg_{(\theta f)} = \frac{v_{fy}}{v_{fx} } = \frac{-10.4}{2.36} = -4.41 (15)[/tex]
⇒ θf = tg⁻¹ (-4.41) = -77.2º
11. Find the direction of the Force
Answer:
We answer that before but I forgot
You are designing a ski jump ramp for the next Winter Olympics. You need to calculate the vertical height h from the starting gate to the bottom of the ramp. The skiers push off hard with their ski poles at the start, just above the starting gate, so they typically have a speed of 2.0 m/s as they reach the gate. For safety, the skiers should have a speed of no more than 30.0 m/s when they reach the bottom of the ramp. You determine that for a 77.0 kg skier with good form, friction and air resistance will do total work of magnitude 4000 J on him during his run down the slope.
Required:
What is the maximum height h for which the maximum safe speed will not be exceeded?
Answer:
h = 40.37 m
Explanation:
We will apply the law of conservation of energy to the skier in this case, as follows:
[tex]Energy\ of\ skier\ at\ the\ gate = Energy\ of\ Skier\ at\ the\ end\\P.E + K.E_{i} = K.E_{f} - W_{friction}\\mgh + \frac{1}{2}mv_{i}^2 = \frac{1}{2}mv_{f}^2 - W_{friction}\\\\mgh = \frac{1}{2}m(v_{f}^2-v_{i}^2) - W_{friction}[/tex]
where,
m = mass of skier = 77 kg
g = acceleration due to gravity = 9.81 m/s²
vf = final speed = 30 m/s
vi = initial speed = 2 m/s
W_friction = Work done by friction and air resistance = 4000 J
Therefore,
[tex](77\ kg)(9.81\ m/s^2)h = \frac{1}{2}(77\ kg)[(30\ m/s)^2-(2\ m/s)^2] - 4000\ J\\\\h = \frac{34496\ J - 4000\ J}{755.37\ N}\\\\[/tex]
h = 40.37 m
Method
1. Place a trolley on a smooth runway and tilt the runway very slightly so that the
slope compensate for the friction between the wheels and the runway. If
pushed gently, the trolley should move at a constant velocity.
2. Measure the mass of the trolleys.
3. Attach the ticker timer to the trolley and thread the tape through the ticker
timer.
4. Attach a smooth pulley vertically to the bottom of the runway.
Answer:
3
Explanation:
it's too because on you measuring mass of something
identify and explain the climate cycle shown
below. Illustrate how conditions change during
the summer
Answer:
wnd change
Explanation: wnd chsnge
Which statement about acceleration is FALSE?
Group of answer choices
A. A car which is slowing down is accelerating
B. When acceleration and velocity are in opposite directions, acceleration is positive
C. If an object changes its direction of motion, its acceleration changes
D. A car which is speeding up is accelerating
8. Two perpendicular forces, one of 45.0 N directed upward and the other of 60.0 N directed to the
right, act simultaneously on an object with a mass of 35.0 kg. What is the magnitude of the
resultant acceleration of the object?
a) 2.14 m/s
b) 5.25 m/s
c) 3.00 m/s
d) 1.41 m/s
Answer:
[tex]a=2.14\ m/s^2[/tex]
Explanation:
Force in upward direction = 45 N
Force in right side = 60 N
Mass of the object, m = 35 kg
Net force on the object is given by :
[tex]F=\sqrt{45^2+60^2} \\F=75\ N[/tex]
We know that,
F = ma
Where
a is acceleration of the object
[tex]a=\dfrac{F}{m}\\\\a=\dfrac{75\ N}{35\ kg}\\\\a=2.14\ m/s^2[/tex]
So, the acceleration of the object is [tex]2.14\ m/s^2[/tex].
pick the correct answer there are three correct answers
15. If a dog pulls a 5 kg sled with a force of 70 N, what is its acceleration?
Answer:
14 m/s^2
Explanation:
We have to use the equation F=ma because the question is a Newton's second law question.
First, list known values
F (force) = 70 N
m (mass) = 5 kg
a (acceleration) = ? (we have to solve for this)
Second, plug in known values into equation.
F=ma
70=5a
Third, solve. To solve this all you have to do is divide both sides by 5
70/5=5/5a
Fourth, your answer will be 14 meters per second squared (m/s^2)
I hope this answer helps and have a great day!
A ball rolls down an inclined plane with a constant acceleration of 2.5 m/s/s. How fast is the ball traveling after 3 seconds
HELP URGENT WILL GIVE BRAINLIEST
Newton discovered that sunlight was composed of colors.
True or False
Answer:
True
Newton's Rainbow. In the 1660s, English physicist and mathematician Isaac Newton began a series of experiments with sunlight and prisms. He demonstrated that clear white light was composed of seven visible colors.
Explanation:
Hope it helps
Which phase of matter makes up stars?
Answer:
Plasma is a phase of matter that makes up stars.
In order to know how a force will affect an object, you must know the _______________.
inertia
weight
direction
gravity
Answer:
needs to know direction
if you dropped your cell phone from a height of 1.20 m above the ground, with what speed would it strike the ground
ωωωωωωωωωωωωωωωωωωωωωωωωωωωωωωωωωωωωωωωωωωωωωωωωωωωωωωωωωωωωωωωωωZ?
Answer: 11.8 m/s
Explanation: Multiply the height, 1.20 m by 9.8. This is because on earth free falling objects have a speed of 9.8 m/s^2 downward.
is the force on a dropped ball.
Ogravity
O acceleration
Answer:
The force applied to any falling object would be gravity. An object cannot fall if there is not gravity; it would simply float.
. The Soviet Yuri Gagarin was the first human to orbit Earth true or false
Answer:
true , I searched and got u the answer
Two cars approach each other from opposite directions each
with a velocity of 54 km/h. One of the cars emits a note of frequency 480 Hz. What will be the approximate frequency
heard in the other car before they cross each other?
Answer:524 Hz
Explanation:
Approximate frequency, heard in other car, when two car approaches each other, before they cross each other is 524 Hz.
What is frequency?Frequency of wave is the number of waves, which is passed thorough a particular point at a unit time.
For the two cars approaching each other the Doppler formula to find the frequency of second car is given as,
[tex]f_2=\dfrac{V_s+V_2}{V_s-V_1}f_1[/tex]
Here, [tex]V_s[/tex] is the speed of the sound.
Two cars approach each other from opposite directions.The velocity of car one is 54 km/h and the velocity of the car two is also 54 km/h.
Convert the unit of velocity of the car as,
[tex]\rm 54km/s=54\times\dfrac{5}{18}m/s\\\rm 54km/s=15m/s[/tex]
As we know that the speed of the sound is 340 m/s and one of the cars emits a note of frequency 480 Hz.
Thus, putting the values in the above formula to find out the frequency heard in the other car before they cross each other as,
[tex]f_2=\dfrac{340+15}{340-15}480\\f_2=524.3\rm Hz[/tex]
The approximate frequency heard in the other car before they cross each other is 524 Hz.
Learn more about the frequency here;
https://brainly.com/question/1436295
magnetism is an example of:
A. contact force
B. non-contact force
C.friction
Answer:
The answer is Non contract force
When you mix red and blue pigment, you produce the color:
orange
black
red
violet
Answer:
violet
Explanation:
given a force of 75N and an acceleration of 3m/s2, what is the mass
force = 75N --- (given)
acceleration = 3m/s² ---- (given)
FORCE = mass × acceleration75N = mass × 3m/s²
mass = 75÷3
mass = 25kg-----------------------------FOLLOW MEAn open pipe is 1.42 m long.
What is the third harmonic
frequency that it produces?
(Speed of sound = 343 m/s)
(Unit = Hz)
please help me guys
Answer:
f(3) = 362.32 Hz
Explanation:
the formula of frequency of open pipe is
f(n) = (n+1)v/2L
n = 0,1,2,3,... (the order)
0 for the first
1 for the second
v = speed of sound
L = the lenght of pipe
f(3) = (2+1) * 343 / 2 * 1,42
f(3) = 3 * 343 / 2.84
f(3) = 362.324 Hz (or you can write 362.32 Hz
Answer: 362.32
Explanation:
Andres buys a new scooter. He goes 8 Km north from the beach. He then
travels 5 Km to the east. Then chases a friend 8 Km north. What distance
did he cover?
What was Andres's displacement?
Answer:
Distance: 21km
Displacement: ~16.76km
By riding an elevator up 200 m, a person’s GPE increases by 164,000 J. What is the person’s mass?
Answer:
Person’s mass M = 83.67 kg (Approx.)
Explanation:
Given:
Gravitational potential energy = 164,000 J
Height = 200 m
Find:
Person’s mass M
Computation:
Gravitational acceleration g = 9.8 m/s²
Gravitational potential energy = mgh
164,000 = (m)(9.8)(200)
Person’s mass M = 83.67 kg (Approx.)
As a ball is released inside Earth's gravitational field and begins to fall to the ground
HELP ASAP PLS
A) there is no gravitational potential energy between them
B) the amount of gravitational potential energy stays the same.
C) the amount of gravitational potential energy increases.
D) the amount of gravitational potential energy decreases.
Answer:
D
Explanation:
forecasted for the miscommunication between range and the other day
If the radius of the Earth decreases to one fourth (1/4) its original size, what would your NEW weight become
1. 4 times as much
2.1/4 as much
3.16 times as much
4.1/16 as much
Answer:
1/4 as much
Explanation:
I don't know the explanation
pick the correct answer
Is the intensity of light directly or inversely proportional to the concentration according to Beer-lambert's law?
Answer:
directly proportional
Explanation:
The Beer-Lambert law states that the quantity of light absorbed by a substance dissolved in a fully transmitting solvent is directly proportional to the concentration of the substance and the path length of the light through the solution.
All of the following are shaped by learned behavior except __________. A. shyness B. blinking C. biting one’s nails D. angry responses
Answer:
B) Blinking .
Explanation:
A ball is thrown vertically upwards with a velocity
of 30 m/s. Find the greatest height attained
A. 40 m B.50 m C.55 m D.45 m
Answer:
Explanation:
The acceleration of gravity is 9.8m/s^2.
So to calculate the time it will take to make the ball stop(which btw means the ball now reach its greatest height), use the formula V1=V0+at. V1 is the final velocity(which is 0), V0 is the starting velocity(which is 30m/s), and the a(cceleration) is 9.8m/s^2.
(You can ignore the fact "at" is -30 instead 30, it's because the directions two velocity travel are opposite. )
We can now know the time it takes to make the ball stop just by the gravitational force is about 3 sec.
Use another formula S=1/2at^2, to find out the S(height) is 1/2*9.8*3^2=44.1, which is approximately D.45m .
Why do you think the Senate requires a greater percentage of votes?
Answer:
yes
Explanation:
yes