1. A vector, V, has a magnitude of 350 N and a direction of 55°.   Determine the following:
   1. V_x = ______
   2. V_y = ______

2. If V_x = 12 m and V_y = 17 m then determine the following:
   1. What is the magnitude, V, of this vector?
   2. What is the direction, θ, of this vector?

3. A hiker walks 2.5 km at an angle of 45 degrees north of west, and then hikes 4.0 km at an angle of 30 degrees north of east.    What is the displacement of the hiker from the origin (magnitude and direction)?   Determine the magnitude and direction by adding the vectors graphically and mathematically.   Be sure to attach your graph.

Magnitude (from graph): _______                                          Magnitude (mathematical) : ______

Direction (from graph):   _______                                             Direction (mathematical) : ______

4. A projectile is launched with a velocity of 130 m/s at an angle of 41 degrees (relative to the ground).   Determine the following:
   1. v_x = _____

2. v_y = _____

3. What is the maximum height of the projectile?

4. What is the range of the projectile?

5. Where is the projectile 4.0 s after it is launched?

6. If there was a 50 m high wall that is 1400 m away, would the projectile be able to clear this wall? Show why or why not.

5. If a river has a westward current of 1.30 m/s and you head due north across the river on a boat that has a speed of 1.5 m/s in still water, then what is speed of the boat relative to the shore?   At what angle does it cross the river?

An electron is placed in a region with a 1010 V/m electric field directed in the positive x-direction. The electron escapes this region after traveling 14.0 cm. What is the kinetic energy of the electron? What is the particle's velocity? Will a proton placed at the same initial position and traveling through a similar 14.0 cm path acquire the same amount of kinetic energy? Will the proton experience the same change in velocity? Why or why not?

I have seen this question on here before but the velocity portion was not present.

A 14.5-μF capacitor is charged to a potential of 40.0 V and then discharged through a 65.0­ Ω resistor.

1. How long after discharge begins does it take for the capacitor to lose 90.0% of its initial charge?

2. How long after discharge begins does it take for the capacitor to lose 90.0% of its initial energy?

3. What is the current through the resistor at the time when the capacitor has lost 90.0% of its initial charge?

4. What is the current through the resistor at the time when the capacitor has lost 90.0% of its initial energy?

Qn 1

A capacitor is attached to a battery with a terminal voltage of V. What happens to the capacitance of the capacitor if it is attached to a new battery with a terminal voltage of 2V, twice as large as the previous battery?

Question 2

A capacitor is attached to a battery with a voltage of V, and a charge Q is pulled from the battery and stored on the capacitor. If a second identical capacitor is attached in parallel with the first, how much total charge has now been pulled from the battery?

Question 3

A capacitor is attached to a battery with a terminal voltage of V. What happens to the charge on the the capacitor if it is attached to a new battery with a terminal voltage of 2V, twice as large as the previous battery?

Question 3 options:

Question 4

Two identical capacitors with capacitance C are connected together in series. How does the capacitance of the combination compare to C?

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Question 5

When current flowing through a resistor increases, the voltage drop across the resistor must be

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Question 6

A certain wire made from a conducting material with resistivity ρ{"version":"1.1","math":"<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>&#x3C1;</mi></math>"} has a certain length, L, and a certain diameter, D, giving it a resistance of R. If a second wire is made from a conductor with a resistivity that is twice as large, and the wire has a length of 2L and a diameter of 2D, how does the resistance of this wire compare to R?

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Question 7

A certain resistor is made of a semiconductor whose temperature coefficient of resistivity is negative. A constant voltage is applied to the resistor, but the resistor heats up significantly as current passes through the wire. What happens to the amount of current the resistor will carry?

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Question 8

A capacitor is attached in series to a resistor with a resistance R. The combination is connected to a battery and allowed to charge. After a certain amount of time, T, the capacitor has charged to 60% of its maximum value. If we repeat the experiment, but replacing the resistor with a new resistor of resistance 2R, what happens to the time it takes for the capacitor to charge to 60% of its maximum value again?

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Question 9

A resistor with a resistance of 3 Ohms is connected in parallel with a resistance with a resistance of 6 Ohms. What is the equivalent resistance of this combination?

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Question 10

In the diagram below, the current flowing through R1 is 0.3 Amps and the current flowing through R2 is 0.1 Amps. What is the current flowing through R3?

Question 10 options:

As part of a liability defence (see the Wikipedia page on Liebeck v. McDonald's for a similar case), lawyers at Tim Hortons have hired you to determine the temperature of a cup of Tim Horton's coffee when it was initially poured. However, you only have measurements of the coffee's temperature taken after it has been purchased. According to Newton's Law of Cooling, an object that is warmer than a fixed environmental temperature will cool over time according to the following relationship:

T(t)=E+(Tinit−E)e−ktT(t)=E+(Tinit−E)e−kt

where EE is the constant environmental temperature, and TT is the temperature of the object at time tt. The object has initial temperature TinitTinit.

Below you are given a data set measured from a purchased cup of coffee. The external temperature of the room is 2020 °C. The temperature of the coffee TiTi is given for several titi, where titi is the time in minutes since the coffee was poured.

Transform the solution T(t)T(t) by putting the exponential term on one side and everything else on the other and taking natural logs of both sides to get:

ln(T(t)−E)=ln(Tinit−E)−kt.ln⁡(T(t)−E)=ln⁡(Tinit−E)−kt.

Now transform the data below in the same way so that you can use linear least squares to estimate the unknown parameters TinitTinit and kk. Fit the transformed data to a line yi=b+axiyi=b+axi, i.e., find the values of aa and bb which minimize f(a,b)=∑i=1((yi)−(b+axi))2f(a,b)=∑i=1((yi)−(b+axi))2:

Use the computed coefficients aa and bb to calculate the following quantities:

What was the initial temperature TinitTinit of the coffee when it was poured?  °C
What is the time constant kk?  /min

A snake of proper length 100 cm is moving at speed v = 0.6c to the right across the table. A mischievous boy, wishing to tease the snake, holds two hatchets 100 cm apart and plans to bounce them simultaneously on the table so that the left hatchet lands immediately behind the snake’s tail 1 .

The boy argues as follows: “The snake is moving with v = 0.6c, therefore, its length measured in my frame is 100cm γ = 80 cm. This implies that the right hatchet will fall 20 cm in front of the snake, and the snake will be unharmed”. On the other hand, the snake argues “the hatchets are approaching me at 0.6c, and the distance between them is 80 cm. Since I am 100 cm long, I will be cut in pieces when they fall” (it’s a very smart snake).

Use Lorentz transformation to resolve this apparent paradox. In other words, resolve it quantitatively, not just with a qualitative argument about non-simultaneity.

Please show work quantitatively, thanks!

A man pushing a crate of mass

m = 92.0 kg

at a speed of

v = 0.845 m/s

encounters a rough horizontal surface of length

ℓ = 0.65 m

as in the figure below. If the coefficient of kinetic friction between the crate and rough surface is 0.351 and he exerts a constant horizontal force of 288 N on the crate.

A man pushes a crate labeled m, which moves with a velocity vector v to the right, on a horizontal surface. The horizontal surface is textured from the right edge of the crate to a horizontal distance ℓ from the right edge of the crate.

(a) Find the magnitude and direction of the net force on the crate while it is on the rough surface.

(b) Find the net work done on the crate while it is on the rough surface.
J

(c) Find the speed of the crate when it reaches the end of the rough surface.
m/s

Q1

A potential difference of 13 V is found to produce a current of 0.45 A in a 3.1 m length of wire with a uniform radius of 0.36 cm. Find the following values for the wire: (a) the resistance (b) the resistivity