A student solving a physics problem for the range of a projectile has obtained the expression r= v20sin(2θ)g where v0=37.2meter/

The Pythagorean Theorem can be utilized here: Imagine a car navigating through traffic—when it turns left to travel north, a right angle of 90 degrees is formed. However, the displacement is always the shortest distance connecting the origin and the endpoint, which forms a triangle in this scenario. In a right triangle, the Pythagorean theorem applies: 215^2+45^2=c^2; therefore, v=√(215^2+45^2).

Since the absolute values of the charges are identical, the changes in potential energy remain equivalent. Consequently, the changes in kinetic energy will also match. We have:

1 = Ke/Kp = m_e * v_e^2 / m_p * v_p^2, which simplifies to:

v_e/v_p = sqrt(m_p/m_e),

indicating that the velocity of the electron is sqrt(m_p/m_e) times greater than that of the proton.

Answer:

The driveway measures 4.98 m

Explanation:

We aim to find the length of the driveway, thus utilizing the following equations

W=ΔK.E    where W represents work and  ΔK.E   indicates the change in kinetic energy

Moreover,

also

W = F.d  where F is the force and d denotes distance

Given that

= 4000 N indicating this frictional force

m = 2100 Kg  

θ= 20.0°  

V=3.8 m/s representing the car's speed at the bottom of the driveway

W=Δ K.E

=  15162  J  

As the x component of gravity is

= mg sinФ

thus

= (2100)(9.8)sin(20.0°) results in

= 7038.77 N

And the Net force is

=

-

= 7038.77 - 4000 = 3038.77 N

So, the length of the driveway equals W / (

) = 15162/3038.77 = 4.98 m

Thus, this is the length of the driveway.

Answer:

(A) = 3.57 m

Explanation:

According to the question, the information provided is:

diameter (d) = 3.2 m

mass (m) = 42 kg

angular speed (ω) = 4.27 rad/s

Using the conservation of energy principle, we have

mgh = 0.5 mv² + 0.5Iω²...equation 1

where

Inertia (I) = 0.5mr²

ω = v/r

Revising equation 1, it turns into

mgh = 0.5 mv² + 0.5(0.5mr²)(v/r)²

resulting in gh = 0.5 v² + 0.5(0.5)v²

This simplifies to 4gh = 2v² + v²

thus h = 3v² ÷ 4g... equation 2

Given ω = v/r, we find v = ωr = 4.27 × (3.2 ÷ 2)

which yields v = 6.8 m/s

Next, substituting the value of v into equation 2 gives us

h = 3v² ÷ 4g

h = 3 × (6.8)² ÷ (4 × 9.8)

h = 3.57 m

Torque = Force * Distance perpendicular

Torque = 15 N * 2 m = 30 Nm