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2 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]2 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.

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You are using a hydrogen discharge tube and high quality red and blue light filters as the light source for a Michelson interfer

boyakko [2]

Answer:

final displacement = +24484.5 nm

Explanation:

The path difference when 158 bright spots were observed with red light (λ1 = 656.3 nm) is given as;

Δr = 2d2 - 2d1 = 150λ1

So, 2d2 - 2d1 = 150λ1

Dividing both sides by 2 to get;

d2 - d1 = 75λ1 - - - - eq1

Where;

d1 = distance between the fixed mirror and the beam splitter

d2 = position of moveable mirror from splitter when 158 bright spots are observed

Now, the path difference between the two waves when 114 bright spots were observed is;

Δr = 2d'2 - 2d1 = 114λ1

2d'2 - 2d1 = 114λ1

Divide both sides by 2 to get;

d'2 - d1 = 57λ1

Where;

d'2 is the new position of the movable mirror from the splitter

Now, the displacement of the moveable mirror is (d2 - d'2). To get this, we will subtract eq2 from eq1.

(d2 - d1) - (d'2 - d1) = 75λ1 - 57λ2

d2 - d1 - d'2 + d1 = 75λ1 - 57λ2

d2 - d'2 = 75λ1 - 57λ2

We are given;

(λ1 = 656.3 nm) and λ2 = 434.0 nm.

Thus;

d2 - d'2 = 75(656.3) - 57(434)

d2 - d'2 = +24484.5 nm

5 0

2 years ago

An electron is moving in the vicinity of a long, straight wire that lies along the z-axis. The wire has a constant current of 8.

viktelen [127]

Answer:

The force that the wire exerts on the electron is $-4.128\times10^{-20}i-6.88\times10^{-20}j+0k$

Explanation:

Given that,

Current = 8.60 A

Velocity of electron $v= (5.00\times10^{4})i-(3.00\times10^{4})j\ m/s$

Position of electron = (0,0.200,0)

We need to calculate the magnetic field

Using formula of magnetic field

$B=\dfrac{\mu I}{2\pi d}(-k)$

Put the value into the formula

$B=\dfrac{4\pi\times10^{-7}\times8.60}{2\pi\times0.200}$

$B=0.0000086\ T$

$B=-8.6\times10^{-6}k\ T$

We need to calculate the force that the wire exerts on the electron

Using formula of force

$F=q(\vec{v}\times\vec{B}$

$F=1.6\times10^{-6}((5.00\times10^{4})i-(3.00\times10^{4})j\times(-8.6\times10^{-6}) )$

$F=(1.6\times10^{-19}\times3.00\times10^{4}\times(-8.6\times10^{-6}))i+(1.6\times10^{-19}\times5.00\times10^{4}\times(-8.6\times10^{-6}))j+0k$

$F=-4.128\times10^{-20}i-6.88\times10^{-20}j+0k$

Hence, The force that the wire exerts on the electron is $-4.128\times10^{-20}i-6.88\times10^{-20}j+0k$

5 0

2 years ago

A large solar panel on a spacecraft in Earth orbit produces 1.0 kW of power when the panel is turned toward the sun. What power

Mandarinka [93]

Answer:

e*P_s = 11 W

Explanation:

Given:

- e*P = 1.0 KW

- r_s = 9.5*r_e

- e is the efficiency of the panels

Find:

What power would the solar cell produce if the spacecraft were in orbit around Saturn

Solution:

- We use the relation between the intensity I and distance of light:

I_1 / I_2 = ( r_2 / r_1 ) ^2

- The intensity of sun light at Saturn's orbit can be expressed as:

I_s = I_e * ( r_e / r_s ) ^2

I_s = ( 1.0 KW / e*a) * ( 1 / 9.5 )^2

I_s = 11 W / e*a

- We know that P = I*a, hence we have:

P_s = I_s*a

P_s = 11 W / e

Hence, e*P_s = 11 W

3 0

2 years ago

Two hockey players skating on essentially frictionless ice collide head-on. Madeleine, of mass 65.0 kg, is moving at 6.00 m/s to

xeze [42]

Explanation:

It is given that,

Mass of Madeleine, $m_1=65\ kg$

Initial speed of Madeleine, $u_1=6\ m/s$ (due east)

Final speed of Madeleine, $v_1=-3\ m/s$ (due west)

Mass of Buffy, $m_2=55\ kg$

Final speed of Buffy, $v_2=3.5\ m/s$ (due east)

Let $u_1$ is the Buffy's velocity just before the collision. Using the conservation of linear momentum as :

$m_1u_1+m_2u_2=m_1v_1+m_2v_2$

$65\times 6+55\times u_2=65\times (-3)+55\times 3.5$

$u_2=-7.13\ m/s$

So, the initial speed of the Buffy just before the collision is 7.13 m/s and it is moving due west. Hence, this is the required solution.

5 0

2 years ago

You and your friend Peter are putting new shingles on a roof pitched at 20degrees . You're sitting on the very top of the roof w

Anit [1.1K]

Answer:

v₀ =3.8 m/s

Explanation:

Newton's second law of the box:

∑F = m*a Formula (1)

∑F : algebraic sum of the forces in Newton (N)

m : mass in kilograms (kg)

a : acceleration in meters over second square (m/s²)

Known data

m=2.1 kg mass of the box

d= 5.4m length of the roof

θ = 20° angle θ of the roof with respect to the horizontal direction

μk= 0.51 : coefficient of kinetic friction between the box and the roof

g = 9.8 m/s² : acceleration due to gravity

Forces acting on the box

We define the x-axis in the direction parallel to the movement of the box on the roof and the y-axis in the direction perpendicular to it.

W: Weight of the box : In vertical direction

N : Normal force : perpendicular to the direction the roof

fk : Friction force: parallel to the direction to the roof

Calculated of the weight of the box

W= m*g = (2.1 kg)*(9.8 m/s²)= 20.58 N

x-y weight components

Wx= Wsin θ= (20.58)*sin(20)° =7.039 N

Wy= Wcos θ =(20.58)*cos(20)°= 19.34 N

Calculated of the Normal force

∑Fy = m*ay ay = 0

N-Wy= 0

N=Wy =19.34 N

Calculated of the Friction force:

fk=μk*N= 0.51* 19.34 N = 9.86 N

We apply the formula (1) to calculated acceleration of the block:

∑Fx = m*ax , ax= a : acceleration of the block

Wx-f = ( 2.1)*a

7.039 - 9.86 = ( 2.1)*a

-2.821 = ( 2.1)*a

a=(-2.821) /( 2.1)

a= -1.34 m/s²

Kinematics of the box

Because the box moves with uniformly accelerated movement we apply the following formula to calculate the final speed of the block :

vf²=v₀²+2*a*d Formula (2)

Where:

d:displacement = 5.4 m

v₀: initial speed

vf: final speed = 0

a : acceleration of the box = -1.34 m/s²

We replace data in the formula (2)

0²=v₀²+2*(-1.34)*(5.4)

2*(1.34)*(5.4)= v₀²

$v_{o} =\sqrt{14.472}$

v₀ = 3.8 m/s

7 0

2 years ago