Menu
CoddyPhysics
START LEARNING
flag En iconEnglishdown icon

Range and Max Height

Part of the Mechanics section of Coddy's Physics journey. Lesson 36 of 94.

On level ground the flight is symmetric:

T = 2 v0 sin θ / g, R = v0 cos θ · T, H = (v0 sin θ)² / 2g

T: time in the air, R: range, H: maximum height.

At the same speed, 30° and 60° give the same range; 60° climbs higher and stays up longer.

Two paths launched from the same point at the same speed, one at 60 degrees and one at 30 degrees. Both land at the same distance R; the 60 degree path rises much higher, to the height H.

Same speed, 30° and 60°: same range R, different maximum height H.

challenge icon

Challenge

A golf ball is hit at 30° above level ground and lands T = 3 s later. Find its launch speed v_0.

Try it yourself

quiz iconTest yourself

This lesson includes a short quiz. Start the lesson to answer it and track your progress.

All lessons in Mechanics

1Vectors and Newton's Laws

Right TrianglesWhat is a Vector?Adding VectorsAxes and DirectionsVector ComponentsForces Around UsFriction and TensionNewton's First LawNewton's Second LawNewton's Third LawRecap - Net Force

4Kinematics in 1D

Position and DisplacementVelocityAccelerationMotion GraphsEquations of MotionRecap - Braking Car

7Kinematics and Newton

From Forces to MotionFrom Motion to ForcesTwo-Stage MotionRecap - Elevator

10Springs

Hooke's LawSprings in SeriesSprings in ParallelRecap - Spring Scale

13Momentum in 2D

Momentum as a Vector2D CollisionsExplosionsRecap - Billiards

16Gravitation

Law of GravitationGravity and AltitudeSatellitesKepler's LawsGravitational EnergyEscape VelocitySatellite EnergyRecap - Mission to Orbit

2Friction

What is Friction?Static FrictionKinetic FrictionFriction and Newton's LawsRecap - Sliding Crate

5Vertical Motion

Free FallThrowing UpwardTime in the AirRecap - Dropped Ball

8Project: Delivery Drone

Mission BriefingTakeoff ThrustClimb to AltitudeCruise and BrakePackage Drop

11Elastic Energy

Elastic Potential EnergySpring LaunchersEnergy with SpringsRecap - Spring Launcher

14Circular Motion

Uniform Circular MotionCentripetal AccelerationHorizontal CirclesVertical CirclesLoop the LoopRecap - Car on a Curve

17Final Challenges

Recap - Stunt RampRecap - Crash TestRecap - Space Probe

3Inclined Planes

Forces on an InclineGravity ComponentsFrictionless InclineIncline with FrictionWill It Slide?Recap - Ramp Challenge

6Projectile Motion

Independent AxesHorizontal LaunchLaunch at an AngleRange and Max HeightRecap - Hit the Target

9Work and Energy

WorkKinetic EnergyWork-Energy TheoremGravitational PEConservation of EnergyPowerRecap - Roller Coaster

12Impulse and Momentum

MomentumImpulseConservation of MomentumElastic CollisionsInelastic CollisionsRecap - Air Track

15Simple Harmonic Motion

What is SHM?Mass on a SpringThe PendulumSHM GraphsEnergy in SHMRecap - Oscillator