While vacationing in the mountains you do some hiking. In the morning, your displacement is S⃗ morning= (2200 m , east) + (4000 m north) + (200 m , vertical). After lunch, your displacement is S⃗ afternoon= (1600 m , west) + (2900 m , north) - (300 m , vertical).

Part A

At the end of the hike, how much higher or lower are you compared to your starting point?

Express your answer with the appropriate units

Part B

What is the magnitude of your net displacement for the day?

Express your answer with the appropriate units.

7. The University Skydiving Club has asked you to plan a stunt for an air show. In this stunt, two skydivers will step out of opposite sides of a stationary hotair balloon 1500 meters above the ground. The second skydiver will leave the balloon 20 seconds after the first skydiver but you want them both to land on the ground at the same time. The show is planned for a day with no wind so assume that all motion isvertical. To get a rough idea of the situation, assume that a skydiver will fall with a constant acceleration of 9.80 m/s2before the parachute opens. As soon as the parachute is opened, the skydiver falls with a constant velocity of 3.2 m/s. If the first skydiver waits 3 seconds after stepping out of the balloon before opening her parachute, how long must the second skydiver wait after leaving the balloon before opening his parachute?

A 65kg skater travelling northward at 3.8m/s accidentally collides with a 75kg skater travelling west at 2.4m/s. They hold on to each other while attempting to regain balance and continue moving in that direction after the collision. What total speed and direction (find angle) do the skaters move together after the collision?

The drive propeller of a ship starts from rest and accelerates at 2.99 x 10-3 rad/s2 for 2.86 x 103 s. For the next 1.90 x 103 s the propeller rotates at a constant angular speed. Then it decelerates at 2.61 x 10-3 rad/s2 until it slows (without reversing direction) to an angular speed of 2.31 rad/s. Find the total angular displacement of the propeller.

Electric Field at a Point

A -70nC charge is distributed uniformly along the x-axis from x = -0.8m to x = 2.6m. Consider a point at y = 1.5m on the y-axis.

a) What is the x-component of the electric field at the point?

b) What is the y-component of the electric field at the point?

c) What is the total magnitude of the electric field at the point?

Thank you

(1)Sphere A is attached to the ceiling of an elevator by a string. A second sphere is attached to the first one by a second string. Both strings are of negligible mass. Here m₁ = m₂ = m = 3.57 kg.

(a) The elevator starts from rest and accelerates downward witha= 1.35 m/s². What are the tensions in the two strings in newtons?

(b) If the elevator moves upward instead with the same acceleration what will be the tension in the two strings in newtons?

(c)The maximum tension the two strings can withstand is 92.2 N. What maximum upward acceleration (in m/s²) can the elevator have without having one of the strings break?

(2) Consider the 65.0-kg ice skater being pushed by two others shown in the figure below.

(a)Find the direction (in degrees counterclockwise from the +x-axis) and magnitude (in N) ofF_totthe total force exerted on her by the others, given that the magnitudes F₁ and F₂ are 22.0 N and 15.8 N, respectively. (AssumeF₁points in the positive x direction.)

(b) What is her initial acceleration (in m/s²) if she is initially stationary and wearing steel-bladed skates that point in the direction ofF_tot?(Assume friction is negligible. Enter the magnitude only.)

(c) What is her acceleration (in m/s²) assuming she is already moving in the direction ofF_tot?(Assume friction is negligible. Enter the magnitude only.)

(3)Here, m_A = 2.50 kg and m_B = 6.50 kg. The string connecting the two objects is of negligible mass and the pulley is frictionless. The objects start from rest and move with constant acceleration.

(a) What is the magnitude of the acceleration (in m/s²) of each of the objects?

(b) What is the magnitude (in N) of the tension in the string?

(c)Through what distance (in m) will the two objects move in the first three seconds of motion?

Two thin slits separated by 0.0880 mm are illuminated by light from a He-Ne laser (? = 633 nm), producing interference fringes on a distant screen. Find the angle between the centers of the central bright fringe and the next bright fringe.

How wide would the slits in Young’s two-slit experiment have to become in order for us to end
up in the double slit diffraction situation? Clearly explain your rationale in a maximum of
three succinct sentences.

The table below contains distance and recessional velocity data for ten galaxies.

1. a) Plot the ‘Hubble Diagram’ for these galaxies. This is simply a plot of the observed velocity on the y-axis and the distance on the x-axis.

2. b) Fit a line to the data that goes through the origin of the plot (that is, where the dis- tanceandvelocityarebothzero). TheslopeofthislineistheHubbleconstant.What is the Hubble constant for these data? NOTE: The value is not the same as the Hubble constant we are adopting in the text.

3. c) Calculate the redshift, ? = ∆?/?& for each galaxy. HINT: Go back to the definition of the Doppler effect in Destination 6 to recall what = ∆?/?& is equal to (or just look at question 1c above). You will see that have the information you need in the table above to calculate the redshift (though, strictly speaking, only for redshifts that are significantly smaller than 1.0).

4. d) Notice that galaxies 2-5 in the table are all at about the same distance, but their ve- locities differ rather significantly. Explain what is likely happening to account for this behavior.

A spelunker is surveying a cave. She follows a passage 120m straight west, then 270m in a direction 45❝ east of south, and then 280 m at 30❝ east of north. After a fourth unmeasured displacement, she finds herself back where she started.

One of the most seemingly obvious things in all of our experiences is that the Earth is still and the Sun moves across the sky. And yet, we are told by science, that the Earth is moving not the Sun. How is it that scientists are so certain about this? This is not a quiz! How do you think this certainty came about?

A trooper is moving due south along the freeway at a speed of 33 m/s. At time t = 0, a red car passes the trooper. The red car moves with constant velocity of 45 m/s southward. At the instant the trooper's car is passed, the trooper begins to speed up at a constant rate of 1.5 m/s2. What is the maximum distance ahead of the trooper that is reached by the red car? m

A filament conductor conducts current I in the −az direction and extends along the entire positive z axis. At origin, it is connected to a conductive blade that forms the xy plane. (a) Determine K on the conductive blade. (b) Use Ampère's circuital law to find H for z> 0. (c) Determine H for z <0.