A.) What is A = (- 1.5, - 3.2) in polar coordinate? B.) What is C = A + B if A =
ID: 1326539 • Letter: A
Question
A.) What is A = (- 1.5, - 3.2) in polar coordinate?
B.) What is C = A + B if A = (1.2, 3.0o) and B = (2.0, 160o)?
C.) Draw a picture of the problem on a sheet of paper and hand it in to be graded.
A baseball is hit with a speed of 27.0 m/s at an angle of 45.0o. It lands on a flat roof of a 13.0-m tall building. If the ball was hit when it was 1.0m above the ground, what horizontal distance does it travel before it lands on the building?
Your picture should have:
1. All moving objects.
2. Each moving object should have a starting position and a final position and any other position of interest along its trajectory for the problem.
3. Your picture should have a coordinate system define.
4. Each object starting position should be labeled with
(a) Starting time
(b) Starting position
(c) Starting velocity
(d) Acceleration
If any quantity is unknown, give it a name. Never use question mark.
5. For each object at any other point in the trajectory, label
(a) The time it arrives there.
(b) The position.
(c) The velocity.
Explanation / Answer
A) |A| = sqrt(1.5^2 + 3.2^2) = 3.534
theta = tan^-1(-3.2/-1.5) = 244.9 degrees
so, A = (3.354, 244.9 degrees)
B) A = 1.2*cos(3) i + 1.2*sin(3)
= 1.198 i + 0.628 j
B = 2*cos(160) i + 2*sin(160)
= -1.88i + 0.684
C = A+B
= -0.682i + 1.312j
|C| = sqrt(0.682^2 + 1.132^2) = 1.48 m
theta = tan^-1(1.312/-0.682)
= 117.5 degrees
so, C = (1.48, 117.5 degrees)
C)
1) given , vo = 27 m/s
voy = vo*sin(45) = 27*sin(45) = 19.09 m/s
vox = vo*cos(45) = 27*cos(45) = 19.09 m/s
let t is the time taken
Apply, h = voy*t + 0.5*g*t^2
(13-1)= 19.09*t - 0.5*9.8*t^2
==> 4.9*t^2 - 19.09*t + 12 = 0
on sloving the above equation we get
t = 3.1 s
so, horizonatl distance traveled, x = vox*t
= 19.09*3.1
= 59.18 m
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