Vector P30 804 103 i cap 760 103 j cap m as suggested in

Vector P_30 = (8.04 * 10^3 i cap + 7.60 * 10^3 j cap) m as suggested in Figure P3.45. Determine the magnitude and orientation of the airplane\'s position vector at t = 45.0 s. In Figure P3.46, the line segment represents a path from the point with position vector (5 vector i + 3 vector j) m to the position with location (16 vector i + 12 vector j) m. Point is along this path, a fraction f of the way to the destination. Find the position vector of point in terms of f. Evaluate the expression from part (a) for f= 0. Explain whether the result in part (b) is reasonable. Evaluate the expression for f= 1. Explain whether the result in part (d) is reasonable.

Solution

a) The difference in x and y co-ordinates between the initial and final points are (16-5)=11 and (12-3)=9 respectively.

Therefore, the position of the point A is (5+11*f)i + (3+9*f)j.

b) For f=0, the point co-ordinates become 5i+3j.

c)This is correct as f=0 refers to the initail point.

d) For f=1, the co-ordinates become 16i+12j.

e)This is correct as for f=1, it refers to the final point.