This paper is a series of five physics problems. The problems cover vectors, deceleration, displacement, and acceleration. The paper includes a vector diagram to explain a Cartesian vector problem. The paper shows all of the work for the problems in the paper and puts the answers in bold.
Displacement, Velocity, And Acceleration
Work out the following problems. Be sure to show your work in detail. See the uploaded files for examples of how the problems should be solved and presented.
A car is driving along a straight section of highway between Oklahoma City and Tulsa. At one point in time, the car is 50 miles from Tulsa. At a later point in time, it's 40 miles from Tulsa. What is its displacement?
s = x-x0
s=10 miles
An aircraft flies 20 km on a course of 030 degrees, then 30 km on a course of 270 degrees. What is its distance and bearing from its takeoff point? (Hints: Make a sketch. Convert flight legs to Cartesian vectors in standard position. See the "Overview of Vectors" handout.)
km at 30O
km at 270O
VR (XRYR)= V1 = V2
Because the second vector is at 270O it makes a right angle with the first vector, so that the length of the resulting vector, VR can be determined with the simple equation a2 + b2= c2
202 + 302 = c2
400+900= c2
c= 36.06km
Then, one can determine the angle of a, the angle including the 30O of the initial angle and whatever the angle is below the x-axis by looking at the sine, which is the opposite leg (30km) over the hypotenuse (36km).
sin O. Of a= 30 / 36.06 = 8.32, therefore a= 56.30 O
56.30 -- 30 = 26.30 O
Therefore, the vector is traveling at 26.30 O. clockwise from the x-axis, but coordinates are measured counter-clockwise in the Cartesian plane, so 360 O -- 26.30 O = 333.77 O
Therefore, the resulting vector is 36.06 km at 333.77 O
3. A snail travels for a year on a straight line, covering 2.7 km. What is its average velocity, in m/s?
2.7km/yr * 1000m/1km * 1 year/365 days * 1 day / 24 hours * 1 hour / 3600 sec=
.0000856164 m/sec
8.56 x 10-5 m/s
4. The parachute on a top fuel dragster slows the car from 300 mph to 100 mph in 5 seconds. What is the average deceleration, in gs (acceleration of gravity)? (Hint: Use an online coversion app, and work in MKS [metric] units.0
d= v1-v2 / t d= 300 mph- 100 mph / 5 sec
d= 200 mph / sec convert:
200 mph* 1m/s = 89.41 m/s
2.237 mph
89.41m/s / 5s = 17.88 m/s2
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