A playground slide is 16 m long and rises at 30°. Enter its vertical height in m.
A javelin leaves a thrower's hand at 20 m/s, aimed 30° above the horizontal. The sketch from the last lesson gives the right triangle: the velocity as hypotenuse, the two components as legs. How long is each leg?
Well, the opener was the whole move: a right triangle's side comes from the hypotenuse and an angle. Multiply by the cosine for the adjacent side, or by the sine for the opposite side.
The horizontal component is the leg adjacent to the launch angle. So the horizontal component is the magnitude times the cosine of the angle.
The vertical component is the leg opposite the launch angle. So the vertical component is the magnitude times the sine of the angle.
For the javelin, the two legs come out like this:
v_x = (20) cos (30°) = 17.3 m/s
v_y = (20) sin (30°) = 10 m/s
Both components come out in the vector's own unit. A velocity in meters per second has components in meters per second. And every launch angle in these component calculations is measured from the horizontal, in degrees.
A stunt plane climbs at 50 m/s, aimed 37° above the horizontal. Calculate the horizontal component of its velocity.
Write down the values in the question:
v = 50 m/s
θ = 37°
v_x = ?
Write down the equation:
v_x = v cos θ
Substitute in the values:
v_x = (50) cos (37°)
Simplify:
v_x = 39.9 m/s
A firework shell launches at 80 m/s, aimed 60° above the horizontal. Calculate the vertical component of its velocity.
Write down the values in the question:
v = 80 m/s
θ = 60°
v_y = ?
Write down the equation:
v_y = v sin θ
Substitute in the values:
v_y = (80) sin (60°)
Simplify:
v_y = 69.3 m/s
Now make the move quick. Six items follow: name the wanted leg, pick the cosine or the sine, and multiply.
A drone flies at 10 m/s, 25° above the horizontal. Enter the horizontal component of its velocity in m/s, to one decimal place.
A drone flies at 10 m/s, 25° above the horizontal. Enter the vertical component of its velocity in m/s, to one decimal place.
A golf ball leaves the tee at 25 m/s, 60° above the horizontal. Enter the horizontal component of its velocity in m/s, to one decimal place.
A golf ball leaves the tee at 25 m/s, 60° above the horizontal. Enter the vertical component of its velocity in m/s, to one decimal place.
A baseball leaves the bat at 14 m/s, 45° above the horizontal. Enter the horizontal component of its velocity in m/s, to one decimal place.
A flare is fired at 60 m/s, 70° above the horizontal. Enter the vertical component of its velocity in m/s, to one decimal place.
A soccer ball is kicked at 35 m/s, 28° above the horizontal. Enter the horizontal component of its velocity in m/s, to one decimal place.
A water jet leaves a fountain at 44 m/s, 55° above the horizontal. Enter the vertical component of its velocity in m/s, to one decimal place.
A model rocket climbs at 50 m/s, 33° above the horizontal. Enter the vertical component of its velocity in m/s, to one decimal place.