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
Reika [66]
3 years ago
14

The particle travels along the path defined by the parabola y=0.5x2, where x and y are in ft. If the component of velocity along

the x axis is vx=(2t)ft/s, where t is in seconds, determine the particle's distance from the origin O. t = 3 s. When t=0, x=0, y=0. Determine the magnitude of its acceleration when t = 3 s.
Engineering
1 answer:
JulsSmile [24]3 years ago
7 0

Answer:

D=41.48 ft

a=54.43\ ft/s^2

Explanation:

Given that

y=0.5 x²                      

Vx= 2 t

We know that

V_x=\dfrac{dx}{dt}

At t= 0 ,x=0  

x=\int V_x.dt

At t= 3 s

x=\int_{0}^{3} 2t.dt

x=[t^2\left\right ]_0^3

x= 9 ft

When x= 9 ft then

y= 0.5 x 9²  ft

y= 40.5 ft

So distance from origin is

x= 9 ft ,y= 40.5 ft

D=\sqrt{9^2+40.5^2} \ ft

D=41.48 ft

a_x=\dfrac{dV_x}{dt}

Vx= 2 t

a_x= 2\ ft/s^2

At t= 3 s , x= 9 ft

y=0.5 x²    

a_y=\dfrac{d^2y}{dt^2}

y=0.5 x²    

\dfrac{dy}{dt}=x\dfrac{dx}{dt}

\dfrac{d^2y}{dt^2}=\left(\dfrac{dx}{dt}\right)^2+x\dfrac{d^2x}{dt^2}

Given that

\dfrac{dx}{dt}=2t

\dfrac{dx}{dt}=2\times 3

\dfrac{dx}{dt}=6\ ft/s

a_y=\dfrac{d^2y}{dt^2}=6^2+9\times 2\ ft/s^2

a_y=54\ ft/s^2

a=\sqrt{a_x^2+a_y^2}\ ft/s^2

a=\sqrt{2^2+54^2}\ ft/s^2

a=54.43\ ft/s^2

You might be interested in
How much metal can be removed from a cracked drum to restore surface
Alisiya [41]

Answer:sc

Explanation:

sc

7 0
3 years ago
Read 2 more answers
A tank with a volume of 8 m3 containing 4 m3 of 20% (by volume) NaOH solution is to be purged by adding pure water at a rate of
lawyer [7]

Answer:

The time necessary to purge 95% of the NaOH is 0.38 h

Explanation:

Given:

vfpure water(i) = 3 m³/h

vNaOH = 4 m³

xNaOH = 0.2

vfpure water(f) = 2 m³/h

pwater = 1000 kg/m³

pNaOH = 1220 kg/m³

The mass flow rate of the water is = 3 * 1000 = 3000 kg/h

The mass of NaOH in the solution is = 0.2 * 4 * 1220 = 976 kg

When the 95% of the NaOH is purged, thus the NaOH in outlet is = 0.95 * 976 = 927.2 kg

The volume of NaOH in outlet after time is = 927.2/1220 = 0.76 m³

The time required to purge the 95% of the NaOH is = 0.76/2 = 0.38 h

4 0
3 years ago
In highways the far left lane is usually the _____
Ivan
Fastest


(Known as the fast lane)
8 0
3 years ago
Read 2 more answers
Give me an A please!!!¡!!!!¡
Andrei [34K]

Answer:

I am in 6th grade why am i in high school things.

Explanation:

8 0
3 years ago
Which of the eight diagnostic steps for locating an engine performance problem is performed first?
Kay [80]

Answer:

D. Perform a thorough visual inspection.

4 0
3 years ago
Other questions:
  • Which of the following manufacturing tools machines parts by moving the part into the cutting tool (instead of moving the cuttin
    13·1 answer
  • How do I calculate the gear ratio​
    6·1 answer
  • A torsional pendulum consists of a 5 kg uniform disk with a diameter of 50 cm attached at its center to a rod 1.5 m in length. T
    13·1 answer
  • What is the thermal efficiency of this reheat cycle in terms of enthalpies?
    11·1 answer
  • La Patrulla Fronteriza de los Estados Unidos analiza la compra de un helicóptero nuevo para la vigilancia aérea de la frontera d
    14·1 answer
  • Chọn dữ liệu phù hợp và biểu diễn chúng dưới dạng biểu đồ, từ đó cho biết 3 yếu tố
    7·1 answer
  • Their game off badminton is always on Tuesday
    11·1 answer
  • Technician A says that fuel filler caps with pressure and vacuum vents are used with EVAP system fuel tanks. Technician B says t
    5·1 answer
  • I) A sag vertical curve is to be designed to join a 4% grade to a 2% grade. If the design
    6·1 answer
  • A company intends to market a new product and it estimates that there is a 20% chance that it will be first in the market
    7·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!