Find the magnitude and direction of the resultant of the addition of the followi

Question

Find the magnitude and direction of the resultant of the addition of the following vectors (magnitude and their directions are given from the x axis( using component method:

A=5m at 15 degree

B= 10 m at 30 degree

C=15 m at 60 degree

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Find (A) the total momentum of the system of two balls A and B when they are rolling towards east with the speed of 12 m/s and 8m/s respectively and have masses 5 K and 3 Kg (B) Do you think these balls will collide to each other, give reasons?

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Given dx/dt bt^p , find x as function of t

Explanation / Answer

1)
Ax = A*cos(15) = 5*cos(15) = 4.83 m

Ay = A*sin(15) = 5*sin(15) = 1.29 m

A = (4.83 i + 1.29 j)m

Bx = B*cos(30) = 10*cos(30) = 8.66 m

By = B*sin(30) = 10*sin(30) = 5 m

B = (8.66 i + 5 j)m

Cx = C*cos(60) = 15*cos(60) = 7.5 m

Cy = C*sin(60) = 15*sin(60) = 12.99 m

C = (7.5 i + 12.99 j)m

A + B +C = (4.83 i + 1.29 j) + (8.66 i + 5 j) + (7.5 i + 12.99 j)

= 20.99 i + 19.28 j

|A+B+C| = sqrt(20.99^2 + 19.28^2)

= 29.5 m <<<<<<-------Answer

direction, theta = tan^-1(19.28/20.99)

= 42.57 degrees <<<<<-----Answer

2) Pnet = PA + PB

= mA*vA + mB*vB

= 5*12 + 3*8

= 84 kg.m/s

B) yes. As vA > vB they collide after some time.

3) dx/dt = b*t^p

dx = b*t^p dt

take integration both sides

integral dx = integral b*t^p*dp

x = b*(t^(p+1)/(p+1)

= b*t^(p+1)/(p+1)

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