Every thrower wants distance. A steep launch buys a long flight but crawls forward. A flat launch is fast forward but drops almost at once. Somewhere between the two extremes there has to be a best angle. Which is it?
A launcher on level ground fires at 20 m/s, with the angle adjustable and air resistance ignored. Three settings get a test shot each, and the landing points are measured.
At 20°, the ball lands 26.2 m out.
At 45°, the ball lands 40.8 m out.
At 60°, the ball lands 35.3 m out.
The middle setting wins. Here is why.
Range is forward speed × time in the air, and the two factors trade against each other: tilting steeper stretches the time but shrinks the forward speed.
Steeper than 45°, the extra hang time no longer pays for the lost forward speed. Shallower than 45°, the extra forward speed no longer pays for the lost time. Either way the range falls.
So a ball thrown at 45° lands farther than the same-speed throw at 20°.
At a kicking contest on level ground, three kicks leave at the same speed: 35°, 45°, and 55°. Air resistance is ignored. Which kick lands farthest?
All three kicks share one launch speed, over level ground with air resistance ignored.
A launch angle of 45° gives the greatest range: it is the best trade-off between horizontal speed and time in the air.
35° and 55° both sit off the best angle, so both land short of the 45° kick.
So the 45° kick lands farthest.
On level ground with air resistance ignored, Lukas kicks two balls at the same speed, one at 45° and one at 18°. Lukas says the 45° kick will land farther away than the 18° kick. Is Lukas correct?
Two throws leave at the same speed over level ground, one at 45° and one at 70°, air resistance ignored. Pia says the 70° throw lands farther out than the 45° throw. Is Pia correct?
A camper hurls a pine cone at 80°, as steeply as she can, hoping the long hang time will carry it far. It lands close by. Why?
Range is forward speed × time in the air.
The 80° launch does stay up a long time.
But it aims almost all of the launch velocity upward, so almost none of it points forward.
The tiny forward speed wastes the long flight, and the pine cone lands close by.
The 80° launch trades away nearly all its forward speed, so the long hang time buys almost no distance.
At a long-toss contest on level ground, throws at one fixed speed land farthest when launched near 45°. Why?
A punter wants his punt to land as far downfield as possible, on level ground with air resistance ignored. At one launch speed, which launch angle should he pick?
A snowball thrown at 25° lands short of a target, on level ground with air resistance ignored. At the same launch speed, which change of angle moves the landing point farther out?
At the same launch speed over level ground, with air resistance ignored, a 65° throw stays in the air longer than a 45° throw. Which statement about the 65° throw is true?