Final answer:
A vector 20.5 cm long represents a force of approximately 47.13 N, calculated using the scale where 8.7 cm represents 20 N.
Step-by-step explanation:
The student's question involves calculating the magnitude of the force represented by a vector of a certain length in the correct direction, given a specific scale. Based on the given scale of 8.7 cm representing 20 N, we can determine that 1 cm represents approximately 2.3 N (20 N divided by 8.7 cm). Therefore, to find the magnitude of the force represented by a vector 20.5 cm long, we need to multiply the length of the vector by the scale factor.
Force represented by the 20.5 cm vector = 20.5 cm * (20 N / 8.7 cm) = 47.126437 N
Thus, a vector that is 20.5 cm long represents a force of approximately 47.13 N when drawn to the same scale.