The launcher from the last lesson is still set to 20 m/s. The 60° shot lands 35.3 m out. Dialed down to 30°, the next shot lands at 35.3 m again. That is exactly the same distance. Is it a coincidence?
Two settings, one landing spot. The explanation sits in the two shots' component splits.
At 20 m/s and 30°, the launch velocity splits into 17.3 m/s forward and 10 m/s upward.
At 20 m/s and 60°, the split is the same two numbers traded: 10 m/s forward and 17.3 m/s upward.
So the 30° shot's forward speed equals the 60° shot's upward speed, and the 60° shot's forward speed equals the 30° shot's upward speed.
One shot is fast and brief. The other is slow and long. The trades cancel, and the two ranges come out equal.
Two angles that add to 90° are called complementary angles. So the two matching launch angles are a complementary pair.
Another pair: 10° and 80°. They add to 90°, so those two shots land at the same spot.
One more: 35° and 80°. That pair adds to 115°, not 90°. Those two shots land at different spots.
The test is always the sum. Add the two launch angles: 90° means equal ranges; any other sum means not.
A launch at 31° lands on a mat, on level ground. At the same launch speed, which other launch angle lands on the mat?
Write down the values in the question:
first launch angle = 31°, same launch speed, level ground
partner angle = ?
Write down the equation:
partner angle = 90° − launch angle
Substitute in the values:
partner angle = 90 − 31
Simplify:
partner angle = 59°
On level ground, a 40° throw and a 50° throw leave at the same speed. Where does the 50° throw land compared with the 40° throw?
A slingshot launch at 25° lands 40 m out on level ground. At the same launch speed, enter the other launch angle, in degrees, that lands 40 m out.
At the same speed over level ground, one ball is thrown at 44° and another at 56°. Do they land at the same spot?
Two launch angles give the same range when they add to 90°.
44° + 56° = 100°.
The sum is not 90°.
No. The angles add to 100°, not 90°, so the ranges differ.
On level ground at the same speed, do a 38° toss and a 62° toss land at the same spot?
Vera tosses a ball at 20°, then tosses it again at the same speed at 70°, over level ground. Vera says the two tosses land at the same spot. Is Vera correct?
On level ground at one launch speed, which pair of launch angles gives two throws that land at the same spot?
A golf chip at 36° lands on the green, 28 m out on level ground. Enter the other launch angle, in degrees, that lands 28 m out at the same speed.
A 15° throw and a 75° throw at the same speed land at the same spot on level ground. Which statement about the two flights is true?