Question

Two arrows are fired horizontally with the same speed of 30.0 m/s. Each arrow has a mass of 0.100 kg. One is fired due east and the other due south. Find the magnitude and direction of the total momentum of this two-arrow system. Specify the direction with respect to due east.

Why do we have to do square root of the Momentum, also at the last to find the direction why we do Tan^-1. Please explain.

Answer 1

P = P1 + P2 where P is a vector quantity

P1 = P2 = .10 kg * 30.0 m/s = 3 kg-m/sec

P = (p1^2 + p2^2)^1/2 add vectors and find magnitude of resultant

p = (3.0^2 + 3.0^2)^1/2 = 4.24 length of resultant vector

Since vectors are at right angles p is the length of the hypotenuse

tan θ = 3.0 / 3.0 = 1 where theta is measured with respect to the positive x-axis and will be below that axis

θ = tan^-1 1 = 45 deg (45 degrees below positive x-axis)

One can find the value of tan θ from the length of the x-y vectors and from tan θ obtain θ