Ask question

Ask question

All categories

2 years ago

11

For the ride to be comfortable, the magnitude of acceleration must not exceed 32 m/s2. What is the fastest constant speed that a

coaster can travel along this section of the track subject to this condition

1 answer:

VMariaS [17]2 years ago

7 0

Answer:

the maximum possible constant speed is 8 m/sec

Explanation:

from the image, Given that

r(t) = (2t, t²,t²/3), -5 ≤ t ≤ 5

Given that the curvature K(t) = 2 / ( t² + 2)²

note that t² + 2 ≥ 2

(t² + 2)² ≥ 4

1 / (t² + 2)² ≤ 1/4

2 / (t² + 2)² ≤ 1/2

Also note that k(0) = 1/2

The normal component of acceleration satisfies aN = kv²

where v = ║v(t)║is the speed of the roller coaster.

The maximum possible normal component of acceleration is 32

so, aN ≤ 32 every where on the track

aN = kv² ≤ 1/2v² ≤ 32

v² ≤ 64

Therefore, the maximum possible constant speed is 8 m/sec

You might be interested in

A positive charge is placed in an electric field that points west. What direction

Leno4ka [110]

Answer:

South

Explanation:

If the electric field points South, then a positive particle is going to be repelled, because field lines point away from the positive end of a magnet. so the positive charge is going to go south. Please mark brainliest!

5 0

1 year ago

Two astronauts on opposite ends of a spaceship are comparing lunches. One has an apple, the other has an orange. They decide to

vesna_86 [32]

Answer:

The speed and direction of the apple is 1.448 m/s and 66.65°.

Explanation:

Given that,

Mass of apple = 0.110 kg

Speed = 1.13 m/s

Mass of orange = 0.150 kg

Speed = 1.25 m/s

Suppose we find the final speed and direction of the apple in this case

Using conservation of momentum:

Before:

In x direction,

$P_{b}=m_{p}v_{p}-m_{o}v_{o}$

$P_{b}=0.110\times1.13-0.150\times1.25$

$P_{b}=−0.0632\ kg-m/s$

In y direction = 0

After:

$v_{ay}$ is velocity of the apple in the y direction

$v_{ax}$ is the velocity of the apple in the x direction

Momentum again:

In x direction,

$0.110\times v_{ax}+0=−0.0632$

$v_{x}=\dfrac{−0.0632}{0.110}$

$v_{x}=−0.574\ m/s$

In y-direction,

$0.110\times v_{ay}-0.150\times0.977=0$

$v_{ay}=\dfrac{0.150\times0.977}{0.110}$

$v_{ay}=1.33\ m/s$

We need to calculate the speed of apple

$v_{a}=\sqrt{(v_{x})^2+(v_{y})^2}$

Put the value into the formula

$v_{a}=\sqrt{(−0.574)^2+(1.33)^2}$

$v_{a}=1.448\ m/s$

We need to calculate the direction of the apple

Using formula of angle

$\tan\theta=\dfrac{v_{ay}}{v_{ax}}$

Put the value into the formula

$\theta=\tan^{-1}(\dfrac{1.33}{0.574})$

$\theta=66.65^{\circ}$

Hence, The speed and direction of the apple is 1.448 m/s and 66.65°.

3 0

2 years ago

Which of the following organisms has an adaptation that will allow it to survive in tundra biome? *

Yakvenalex [24]

Answer:

the awnser is A becuse the hair help.

6 0

2 years ago

Compare the pressure exerted by the liquid at points A, B and C. Justify your answer

zzz [600]

Answer:

Pressure is equal in A, B, C and D

Explanation:

Pressure does not depends on the shape of the container

Pressure acting all direction

5 0

2 years ago

While moving in, a new homeowner is pushing a box across the floor at a constant velocity. The coefficient of kinetic friction b

Citrus2011 [14]

Answer:

$\theta = 66.7 degree$

Explanation:

since force is applied downwards at some angle with the horizontal

so here we will have

$F_n = mg + Fsin\theta$

now we know that the box will not move if applied force is balanced by frictional force on it

so we will have

$Fcos\theta = \mu F_n$

$F cos\theta = \mu (mg + F sin\theta)$

$F(cos\theta - \mu sin\theta) = \mu mg$

$F = \frac{\mu mg}{cos\theta - \mu sin\theta}$

so here we can say

$cos\theta - \mu sin\theta > 0$

$tan\theta = \frac{1}{\mu}$

$\theta = tan^{-1}\frac{1}{\mu}$

$\theta = tan^{-1}(\frac{1}{0.43})$

$\theta = 66.7 degree$

6 0

2 years ago