Speed Question

Question

Joe and his dog Freddie are in a park with Joe standing 60 feet due south of Freddie. Freddie starts to run due east and without stopping or changing direction, catches a ball thrown to him by Joe. If the ball was in the air for three seconds and the ball went three times as fast as Freddie, how fast did Freddie run? Simply your answer

Answer 1

I am assuming that Freddie starts to run at the same time that Joe throws the ball.

 

v1 = speed of Freddie

 

v2 = speed of ball = 3*v1

 

t = time ball is flying = 3 s

 

Then Freddie moves east a distance d = v1*t = 3*v1 ft

 

The ball moves northeast a distance v2*t = (3*v1)(t) = (3*v1)(3) ft = 9*v1 ft

 

The path of the ball forms a hypotenuse with 60 ft and 3*v1

 

(9*v1)^2 = (60)^2 + (3*v1)^2

 

81*v1^2 = 3600 + 9*v1^2

 

72*v1^2 = 3600

 

v1 = sqrt(3600/72) ft/s = 7.071 ft/s, which is Freddie's speed