Question

A quarterback takes the football from the line of scrimmage and runs backward for 15 meters, he then runs sideways parallel to the line of scrimmage for 12 meters. At this point he throws the ball 50 meters perpendicular to the line of scrimmage where it is caught by the receiver. How far is the football from its original position?

Answer 1

65 meters from the original position

Answer 2

A quarterback ... runs backward for 15 meters,

=> displacement vector = -15 j

he ... runs sideways parallel to the line of scrimmage for 12 meters.

=> displacement vector = 12 i

he throws the ball 50 meters perpendicular to the line of scrimmage

=> displacement vector = 50j

where it is caught by the receiver.

=> net displacement = -15j + 12i + 50j = 12i + 35j

How far is the football from its original position?

distance ^2 = (12m)^2 + (35m)^2 = 1,369 m^2

=> distance = √ (1,369m^2) = 37 m^2

Answer: 37 m^2