Ask question

Ask question

All categories

3 years ago

9

Vinny is on a motorcycle at rest, 200 m away from a ramp that jumps over a gully. Calculate the minimum constant acceleration Vi

nny must have to get to the ramp in 8 s before his pursuers catch up with him.

1 answer:

soldier1979 [14.2K]3 years ago

7 0

Answer: 6.25 m/s^2

Explanation:

The distance between Vinny and the ramp is 200m

And he has 8 seconds (At max) to reach that distance.

The initial velocity is 0m/s

The initial position is 0m

Now, we want to find the constant acceleration in order to do this, so suppose that we have a constant acceleration A.

a(t) = A.

To have the velocity, we must integrate over time, and remember that the constant of integration is equal to zero because the initial velocity is zero.

v(t) = A*t

For the position, we integrate again over time.

p(t) = 0.5*A*t^2

And we want to travel 200m in 8 seconds, then:

p(8s) = 200m

0.5*A*(8s)^2 = 200m

A*32s^2 = 200m

A = 200m/32s^2 = 6.25 m/s^2

This is the minimum acceleration in order to do this, if Vinny has a larger acceleration he will travel the 200m in a smaller time.

You might be interested in

Problem One: A beam of red light (656 nm) enters from air into the side of a glass and then into water. wavelength, c. and speed

Ivanshal [37]

Answer:

Part a)

$f_w = f_g = 4.57 \times 10^{14} Hz$

Part b)

$\lambda_w = 492 nm$

$\lambda_g = 437.3 nm$

Part c)

$v_w = 2.25 \times 10^8 m/s$

$v_g = 2.0 \times 10^8 m/s$

Explanation:

Part a)

frequency of light will not change with change in medium but it will depend on the source only

so here frequency of light will remain same in both water and glass and it will be same as that in air

$f = \frac{v}{\lambda}$

$f = \frac{3 \times 10^8}{656 \times 10^{-9}}$

$f = 4.57 \times 10^{14} Hz$

Part b)

As we know that the refractive index of water is given as

$\mu_w = 4/3$

so the wavelength in the water medium is given as

$\lambda_w = \frac{\lambda}{\mu_w}$

$\lambda_w = \frac{656 nm}{4/3}$

$\lambda_w = 492 nm$

Similarly the refractive index of glass is given as

$\mu_w = 3/2$

so the wavelength in the glass medium is given as

$\lambda_g = \frac{\lambda}{\mu_g}$

$\lambda_g = \frac{656 nm}{3/2}$

$\lambda_g = 437.3 nm$

Part c)

Speed of the wave in water is given as

$v_w = \frac{c}{\mu_w}$

$v_w = \frac{3 \times 10^8}{4/3}$

$v_w = 2.25 \times 10^8 m/s$

Speed of the wave in glass is given as

$v_g = \frac{c}{\mu_g}$

$v_g = \frac{3 \times 10^8}{3/2}$

$v_g = 2 \times 10^8 m/s$

4 0

3 years ago

Could a person at the south pole see the north star, explain??

9966 [12]

Answer:

If conditions are just right, you can see Polaris from just south of the equator. Although Polaris is also known as the North Star, it doesn't lie precisely above Earth's North Pole. If it did, Polaris would have a declination of exactly 90 degree.

Explanation:

4 0

2 years ago

Read 2 more answers

Compute the size of the charge necessary for two spheres separated by 1m to be attached with the force of 1N. How many electrons

yarga [219]

Answer:

$q\approx 6.6\cdot 10^{13}~electrons$

Explanation:

<u>Coulomb's Law</u>

The force between two charged particles of charges q1 and q2 separated by a distance d is given by the Coulomb's Law formula:

$\displaystyle F=k\frac{q_1q_2}{d^2}$

Where:

$k=9\cdot 10^9\ N.m^2/c^2$

q1, q2 = the objects' charge

d= The distance between the objects

We know both charges are identical, i.e. q1=q2=q. This reduces the formula to:

$\displaystyle F=k\frac{q^2}{d^2}$

Since we know the force F=1 N and the distance d=1 m, let's find the common charge of the spheres solving for q:

$\displaystyle q=\sqrt{\frac{F}{k}}\cdot d$

Substituting values:

$\displaystyle q=\sqrt{\frac{1}{9\cdot 10^9}}\cdot 1$

$q = 1.05\cdot 10^{-5}~c$

This charge corresponds to a number of electrons given by the elementary charge of the electron:

$q_e=1.6 \cdot 10^{-19}~c$

Thus, the charge of any of the spheres is:

$\displaystyle q = \frac{1.05\cdot 10^{-5}~c}{1.6 \cdot 10^{-19}~c}$

$\mathbf{q\approx 6.6\cdot 10^{13}~electrons}$

5 0

2 years ago

A crane exerts a net force of 900 N upward on a 750-kilogram car as the crane starts to lift the car from the deck of a cargo sh

melisa1 [442]

Answer: 1.2m/s^2

Explanation: the force exerted on the car is 900N upwards

The mass of the car is 750kg

According to Newton's third law acceleration is proportional to force

F = ma

900 = 750a

a = 900/750

a = 1.2m/s^2

5 0

3 years ago

A baseball has a mass of 0.15 kg and radius 3.7 cm. In a baseball game, a pitcher throws the ball with a substantial spin so tha

mylen [45]

Answer:

Rotational kinetic energy = 0.099 J

Translational kinetic energy = 200 J

The moment of inertia of a solid sphere is $I = \frac{2}{5}mr^2$ .

Explanation:

Rotational kinetic energy is given by

$\text{RKE} = \frac{1}{2}I\omega^2$

where <em>I</em> is the moment of inertia and <em>ω</em> is the angular speed.

For a solid sphere,

$I = \frac{2}{5}mr^2$

where <em>m</em> is its mass and <em>r</em> is its radius.

From the question,

<em>ω</em> = 49 rad/s

<em>m</em> = 0.15 kg

<em>r</em> = 3.7 cm = 0.037 m

$\text{RKE} = \frac{1}{2}\times \frac{2}{5} mr^2\omega^2 = \frac{1}{5} mr^2\omega^2$

$\text{RKE} = \frac{1}{5} (0.15\ \text{kg})(0.037\ \text{m})^2(49\ \text{rad/s})^2 = 0.099\text{ J}$

Translational kinetic energy is given by

$\text{TKE} = \frac{1}{2} mv^2$

where <em>v</em> is the linear speed.

$\text{TKE} = \frac{1}{2} (0.15\ \text{kg})(52\ \text{m/s})^2 = 200\text{ J}$

5 0

3 years ago

Read 2 more answers