Question

A snow ball, mass m, is launched with an initial velocity ~v0 and lands back on a ground at a distance D from the launch point. a) Show that there are 2 launch angles θhi and θlo which achieve the same range D for the same launch speed. Calculate these angles as a function of the given variables. b) Calculate the difference in time-of-flight ∆ttof between the two trajectories. Discuss the pros and cons of each trajectory, imagining different real life situations. c) Numerically evaluate these ballistic characteristics, if v0 = 15 m/s and D = 20 m

Answer 1

(a)

Range of projectile (D)

So

D₁= D₂

_if

_{This equation has two solution}

_either

_Or

_So

_{for two angles}

_{range will be same}

_{b) Again time of flight}

_{So for both values of angle}

_{So time of flight will be different for both values of angle . For acute angle time of flight will be small and for obtuse angle time of flight will be large .}

_{c) putting all the values we get}

So

Time period for 30°

T=2×15sin30°/g=1.53 s

Time period for 60°

T=2×15×sin60/g=2.65 s

∆T=1.12 s