Problema Solution
The semifinal of the 1999 women's world cup soccer match is being played at Stanford stadium on the fourth of July. Mia Hamm, star of the united states team, has just received the ball on a breakaway. She is 60 yards from Brazil's goal. Brazilian start Sissi is the closest opponent to Hamm and is 10 yards behind her. Mia takes off for Brazil's goal and, while dribbling the ball, is able to run at a speed of 6.8 yards per second. Sissi takes off at the same time that Hamm does and runs at 8.4 yards per second. Hamm has decided to shoot at the same exact moment that Sissi catches up to her. How far away from the goal will Hamm be when she shoots?
Answer provided by our tutors
let
v1 = 6.8 yps the speed of Hamm
v2 = 8.4 yps the speed of Sissi
t = the time between the take off and the shot
since speed = distance/time => distance = speed*time
v1*t + 10 = v2*t
6.8t + 10 = 8.4t
by solving we find
t = 6.25 s
click here to see the step by step solution of the equation
after t = 6.25 s the distance between Hamm and the goal when she takes the shot is
60 - v1*t = 60 - 6.8*6.25 = 17.5 yards.