Question

A halfback is initially running south at a speed of 8.70 m/s, quickly cuts to his right, and 0.520 s later is running 60.0° west of south at 8.00 m/s. Find his average acceleration.

magnitude

direction north of west

Answer 1

Halfback is running initially South with a speed of v1 = 8.70 m/s and later at time t = 0.520 s,

cuts to right means in the west direction running 60.0° west of south at v2 = 8.00 m/s.

if we write these in the vector form taking the +x axis as reference axis

V1 = 8.7 cos 270 i + 8.7 sin 270 j

v2 = 8.0 cos 240 i + 8.0 sin 240 j

V1 = 0 m/s i - 8.7 m/s j

V2 = - 4 m/s i -6.9282 m/s j

the average acceleration is a = v2-v1/(t2-t1) = dv/dt

   a = (1/0.520)(-4 m/s i +(-6.9282-(-8.7))m/s j )

   a = (1/0.520)(-4 m/s i + 1.7718 m/s j)
  
   a = -7.6923 m/s^2 i + 3.4073 m/s^2 j

magnitude is

   a = sqrt((-7.6923)^2+3.4073^2) m/s2
   a = 8.4132 m/s2
direction is

   theta = arc tan (ay/ax)

   theta = arc tan ((3.4073)/(-7.6923))
  
   theta = -23.89 degrees
North of west