2: Please answer ONL.Y 4 out of 5 Essay Questions (15 points each). Part 2: Plea

Question

2: Please answer ONL.Y 4 out of 5 Essay Questions (15 points each). Part 2: Please answer Please read the questions carefully and give carn full crodit for the problems questions carcfully and give detailed answers to the questions asked You have to show all your work to Vectors A B C 1. Vectors A, B, andhave the following components, expressed in arbitrary units: B and C component compone compone nnt +3.0 +4.0 2.0 +2.0 +2.0 +2.0 nt Vector C is defined so that A 9B - Find the magnitude of C 7 As (2.0 (a (-2.0 (20 2. A particle decelerates uniformly from a speed of 30 cm/s to rest in a time interval of 5.0s. It then has a uniform acceleration of 10 cm/s' for another 5s. The particle moves in the same direction along a straight line. Find the average speed over the whole time interval? 30 tm 00 cn 100 6.66 m/s

Explanation / Answer

1)

A = 3 i + 4 j -2 k

B = 2 i + 2 j + 2 k

A - 9 B + C = 0

C = 9B - A

C = 9 *(2 i + 2 j + 2 k ) - (3 i + 4 j -2 k )

C = 15 i+ 14 j + 20 k

magnitude of C = sqrt(15^2 + 14^2 +20^2 )

magnitude of C = 28.7 nt

2)

time taken , t = 5 s

acceleration ,a = 10 cm/s^2

speed , v = 30 cm/s

let the total distance is d

d = 30 * 5 + 0.5 * 10 * 5^2

d = 275 cm

average speed = 275 cm/5s

average speed = 55 cm/s

the average speed is 55 cm/s

3)

initial speed , u = 15 m/s

time taken , t = 16 s

let the height is h

using second equation of motion

h = | 15 * 16 - 0.5 * 9.8 * 16^2 |

h = 1014.4 m

the height of helicopter is 1014.4 m

4)
let the time taken to fall is t

10 = 6 * sin(30) * t + 0.5 * 9.8 * t^2

solving for t

t = 1.15 s

horizontal distance = 1.15 * 6 * cos(30)

horizontal distance = 6 m

the tile will land 6 m away

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