Question

A soccer ball is kicked from the ground with an initial speed of 14.5 m/s. After 0.272 seconds, ts speed is 12.4 m/s. (A) Give a strategy that will allow you to calculate the ball's initial direction of motion. (B) Use your strategy to find the initial direction.

Answer 1

v₀⒳= v₀•cosα,
v₀⒴ =v₀•sinα,
v₀² =v₀⒳² +v₀⒴²,
v² =v⒳² +v⒴²,
v⒳= v₀⒳,
v⒴=v₀⒴ -g•t,
v² =v⒳² +v⒴² = v₀⒳²+(v₀⒴ -g•t)²=
=v₀⒳²+v₀⒴² -2 v₀⒴•g•t +(g•t)² =
= v₀²-2 v₀•sinα•g•t +(g•t)².
sinα= [v₀²-v²+(g•t)²]/2•v₀•g•t =
=[14.5² -12.4²+(9.8•0.272²]/(2•14.5•9.8•0.272) =
=0.823.
α=55.35°