Time of Flight and Vertical Timing
The flight time is obtained from y_f - y_0 = u_y T - one-half gT squared. When y_f = y_0, the nonzero root is T = 2u sin theta/g.
Why this shows up in the exam
Scheduling interception at a height · Comparing projectiles with different angles · Finding launch components from ascent time
Learn the idea
Flight timing is controlled entirely by the vertical component and the chosen final height. Horizontal motion decides where the projectile lands, but vertical motion decides when it reaches a level. Equal launch and landing heights give a symmetric up-and-down time.
🧠 Memory hook: Time comes from vertical motion; equal levels make ascent and descent times match.
Get this one clearly and it pays off every single time it shows up in the paper. 🎯
Formulas & facts to keep ready
- Delta y = u_y T - (1/2)gT² — general vertical timing equation
- T = 2u sin(theta)/g — flight time for equal launch and landing levels
- t_up = u sin(theta)/g — time to the highest point
How to approach it
- 1Write the vertical displacement with signs
- 2Solve the time equation and reject nonphysical roots
- 3Use horizontal motion only after the time is known
Common slip-ups that cost marks
- •Using equal-level time for an elevated landing
- •Taking the zero root as the flight time
- •Using horizontal speed in the vertical timing equation
🌟 That's the whole idea — you've got this. Try the practice set below; every question you attempt makes it stick a little harder.
Original chapter practice
Original questions for this chapter, not past-paper questions or an exact mapping to this individual concept.
A particle has initial speed 2 m/s and constant acceleration 3 m/s^2 for 4 s. What distance does it cover?
More from Kinematics
Distance, Displacement, Speed, and Velocity
Understand the differences between distance and displacement, and between speed and velocity, including how to calculate average speed and average velocity in various scenarios.
Equations of Motion and Uniform Acceleration
Learn the kinematic equations for uniformly accelerated motion, including applications to free fall, retardation, and calculation of distance in specific time intervals.
Projectile Motion
Study the motion of projectiles, including the independence of horizontal and vertical components, trajectory equations, maximum height, and the effect of initial conditions.
Relative Velocity and Motion Analysis
Explore how to determine the velocity of one object relative to another and analyze motion from different reference frames, including periodic motion.
Position, Path Length, and Displacement
For one-dimensional motion, displacement over an interval is Delta x = x_f - x_i and may be positive, negative, or zero. Distance is the non-negative path length, so distance is always at least |Delta x|.
Speed and Velocity
Instantaneous velocity is the signed rate v = dx/dt, while instantaneous speed is |v|. In one dimension the sign of v identifies motion along or opposite the positive axis.