Two perpendicular displacements: 7 m south and 24 m east. Enter the resultant's magnitude in m.
Two perpendicular displacements: 20 m east and 11 m north. Enter the resultant's angle north of east, to the nearest degree. Answers within 1° are accepted.
Partway through its flight, a ball launched horizontally from a rooftop moves sideways at 12 m/s and downward at 5 m/s. The ball has one velocity, not two. What are its speed and direction at that moment?
The sketch from the last lesson showed the two component arrows at every point: an unchanging horizontal arrow, and a vertical arrow that free fall grows. Speed and direction come from recombining the two arrows: magnitude by the Pythagorean theorem, direction by the tangent.
The two components are perpendicular, so the speed is the hypotenuse of their right triangle:
v = √(12² + 5²) = √169 = 13 m/s
The direction comes from the tangent of the angle below the horizontal:
tan θ = 5 ÷ 12, so θ = tan⁻¹(5 ÷ 12) ≈ 23°
A stone thrown horizontally from a bridge moves, at one moment, 8 m/s horizontally and 6 m/s downward. Calculate its speed at that moment.
Write down the values in the question:
v_x = 8 m/s
v_y = 6 m/s downward
v = ?
Write down the equation:
v = √(v_x² + v_y²)
Substitute in the values:
v = √(8² + 6²) = √100
Simplify:
v = 10.0 m/s
The same stone: v_x = 8 m/s, v_y = 6 m/s downward. Calculate the angle of its velocity below the horizontal.
Write down the values in the question:
v_x = 8 m/s
v_y = 6 m/s downward
θ = ?
Write down the equation:
tan θ = v_y ÷ v_x
Substitute in the values:
tan θ = 6 ÷ 8
Simplify:
θ = tan⁻¹(6 ÷ 8) = 36.9° below the horizontal
Late in its flight off a cliff, a ball moves 20 m/s horizontally and 21 m/s downward. Enter its speed at that moment in m/s, to one decimal place.
The same moment: v_x = 20 m/s, v_y = 21 m/s downward. Enter the angle of the ball's velocity below the horizontal, in degrees to one decimal place.
Early in its flight off a rooftop, a baseball moves 24 m/s horizontally and 7 m/s downward. Enter its speed at that moment in m/s, to one decimal place.
At one moment of its flight off a pier, a fishing float moves 9 m/s horizontally and 12 m/s downward. Enter its speed at that moment in m/s, to one decimal place.
Shortly after leaving a shelf, a marble moves 5.0 m/s horizontally and 2.0 m/s downward. Enter the angle of its velocity below the horizontal, in degrees to one decimal place.
A ball leaves a cliff top horizontally at 10 m/s. It is still in the air 2.0 s later. Enter its speed at that moment in m/s, to one decimal place.