Answer:
I. Angle = 41.7° Northeast.
II. Vr = 7.08m/s
Explanation:
Let the two cars be denoted by A and B
<u>Given the following data;</u>
Mass of car A = 1232 Kg
Velocity of car A = 25.6 m/s
Mass of car B = 2028 Kg
Velocity of car B = 17.5m/s
First of all, we would solve for momentum;
Momentum = mass × velocity
Momentum, M1 = 1232 × 25.6
Momentum, M1 = 31539.2 Kgm/s
Momentum, M2 = 2028 × 17.5
Momentum, M2 = 35490 Kgm/s
Now, let's find the resultant momentum using the Pythagoras theorem;
R² = M1² + M2²
R² = 31539.2² + 35490²
R² = 994721136.6 + 1259540100
R² = 2254261237
Taking the square root of both sides, we have
Resultant momentum, R = 47479.06 Kgm/s
To find the direction;
Angle = tan¯¹(M1/M2)
Angle = tan¯¹(31539.2/35490)
Angle = tan¯¹(0.89)
<em>Angle = 41.7° Northeast.</em>
To find the speed;
R = (M1 + M2)Vr
47479.06 = (31539.2 + 35490)Vr
47479.06 = 67029.2Vr
Vr = 47479.06/67029.2
<em>Vr = 7.08m/s</em>
