In this question, use g=9.8 m s−2g = 9.8 \text{ m s}^{-2}g=9.8 m s−2.
A pyrotechnic shell is fired from a launch tube at ground level with an initial velocity of 21 m s−121 \text{ m s}^{-1}21 m s−1 at an angle α\alphaα to the horizontal.
The shell reaches a maximum vertical height of HHH metres.
Show that
H=22.5sin2α H = 22.5 \sin^2 \alpha H=22.5sin2αIn a specific display, the launch angle is constrained such that 0∘≤α≤60∘0^\circ \le \alpha \le 60^\circ0∘≤α≤60∘. Determine the maximum possible height HHH the shell can reach under these conditions.
A technician suggests that using a more massive shell would result in a lower maximum vertical height when launched with the same velocity and angle. Explain whether the technician is correct according to the standard projectile model.
91 exam-style questions on OCR (MEI) A Level Maths 3.3 Projectiles (A-level only), covering 3.3.1 Model motion under gravity using vectors (A-level only), 3.3.2 Position, velocity, range and maximum height (A-level only), 3.3.3 Find the initial velocity of a projectile (A-level only), 3.3.4 Equation of the trajectory (A-level only), and 3.3.5 Solve simple projectile problems (A-level only). Each one has a worked solution and a mark scheme showing where the marks go.