A research team wishes to develop a symbolic model for the flight time of a…
PHYSICS · Multi-part · A Level · Physics · Mechanics and materials · Mechanics and materials
Problem
A research team wishes to develop a symbolic model for the flight time of a projectile launched from height y0 above the ground with initial speed v0 at an angle θ above the horizontal. The projectile lands on ground that is Δy below the launch height (that is, the landing point is at vertical position y=y0−Δy with Δy>0). Air resistance is negligible; the acceleration due to gravity is g.
Complete the following theoretical analysis before testing the model with numerical values.
(a) Derive an explicit expression for the total flight time tflight in terms of v0, θ, g, and Δy.
(b) Show algebraically that when Δy=0 your expression reduces to the familiar result for symmetrical projectile motion.
(c) Using your expression from part (a), calculate the flight time for a rock launched from a 6.0m-high platform with speed 22.0m/s at 40∘ above the horizontal if it lands on the ground below the platform.