Help Chapter 4, ProDICIH Part B I will grade these problems. Each written proble

Question

Help Chapter 4, ProDICIH Part B I will grade these problems. Each written problem in this part is worth 10 points, for a total of 30 points for this part. A certain particle's position vector is given by R(t) = Rx(t) + Ry(t), where Rx(t) = 3t2-6t, and Ry(t) = 2t. a) What is the magnitude and direction of the position vector at t = 1s and t = 2s? b) What is the magnitude and direction of the velocity vector at t = 1s and t = 2s? I. Aidyn is playing with his toy cars on the kitchen table, and sends one flying off the table. The car lands on the floor a horizontal distance of 1.5 meters from the edge of the table. The table is 1 m tall. a) For how much time was the car in the air? b) What was the initial speed of the toy car? 2.

Explanation / Answer

Rx(t) = 3t^2 - 6t
Ry(t) = 2t

1)

(a)
Rx(1) = 3*1^2 - 6*1 = 3 - 6 = -3
Ry(1) = 2*1 = 2

R = -3 i + 2 j

Magnitude = ((-3)^2 + 2^2)^(1/2) = 3.61
Angle = Arctan(2/-3) = -33.69 degrees

Rx(1) = 3*2^2 - 6*2 = 12 - 12 = 0
Ry(1) = 2*2 = 4

R = 0 i + 4 j

Magnitude = ((0)^2 + 4^2)^(1/2) = 4
Angle = 90 degrees

(b)
Vx(t) = d(Rx(t))/dt = 6t - 6
Vy(t) = d(Ry(t))/dt = 2

Vx(1) = 6*1 - 6 = 0
Vy(1) = 2

V(1) = 0 i + 2 j

Magnitude = 2
Angle = 90 degrees

Vx(2) = 6*2 - 6 = 6
Vy(1) = 2

V(1) = 6 i + 2 j

Magnitude = ((6)^2 + 2^2)^(1/2) = 6.324
Angle = 18.43 degrees

Please post the second question separately.

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