4.32

(a) Show that for a projectile the angle between the velocity and the x-axis as a function

of time is given by

(b) Shows that the projection angle _0 for a projectile launched from the origin is

given by

where the symbols have their usual meaning.

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Vishal Baghel | Contributor-Level 10

8 months ago

4.32

(a) Let $θ (t) = \tan^{- 1} ? (\frac{v_{o y} - g t}{v_{o x}})$ be the angle at which the projectile is fired w.r.t. the x-axis, since $θ_{0} = \tan^{- 1} ? (\frac{4 h_{m}}{R})$ depends on t

Therefore tan $θ$ since (Vy=Voy -gt and Vx = Vox)

(b) Since $θ$ = $θ (t) = \frac{V x}{V y} = \frac{V o y - g t}{V o x}$ sin2 $θ (t) = \tan^{- 1} ? (\frac{V o y - g t}{V o x})$ /2g…….(1)

R = $h_{m a x}$ sin2 $u^{2}$ /g …….(2)

Dividing (1) by (2)

( $θ$ /R) = [ $u^{2}$ sin2 $θ$ /2g]/[ $h_{m a x}$ sin2 $u^{2}$ /g] = $θ$ / 4

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