A Nordic jumper goes off a ski jump at an angle of 10.0° below the horizontal, traveling 92.0 m horizontally and 47.0 m vertically before landing.; (a) Ignoring friction and aerodynamic effects, calculate the speed needed by the skier on leaving the ramp

Answer 1

v(x) =x/t =>
t=x/v⒳=x/v₀•cosα
y=v₀⒴•t +gt²/2 =
= v₀⒴• x/v₀•cosα +g•x²/2v₀²•cos²α=
=x•tanα + g•x²/2v₀²•cos²α.
v₀=sqrt{g•x²/2•cos²α(y-x•tan α)}=
=sqrt{9.8•92²/2•0.97•(47-92•tan10)}=
=37.3 m/s.

Answer 2

A rowboat crosses a river with a velocity of 4.23 mi/h at an angle 62.5o north of west relative to the water. The river is 0.543 mi wide and carries an eastward current of 0.73 mi/h. How far upstream is the boat when it reaches the opposite shore?