1. A particle is projected with a speed V, from a height h, above a horiztonal plane, at an angle of θ to the horizontaal.
(a) if its range on the horizontal plane is R, show that:
R^2sec^2θ -[2V^2R/g](tanθ)- [2hV^2/g] = 0
(b) without solving this equation, show that it has one negative root. Interpret the results.
(c) show that the maximum range for a given V is {V^2 + V[(V^2 +4hg)]^(1/2)}/2g, given the maximum range occurs when it is projected at θ = pi/4
2. (a) A particle is projected from ground level to just clear two walls of hiehgt 7m, and distant 7 metres and 14 metres from the point of projection. Prove that if θ is the angle of projection, then tanθ =3/2. Assume g = 10 m/s^2 and no air résistance
(b) Prove that if the walls are h metres high and distant b metres, and c metres from the pointof projection, then tanθ = h(b+c)/bc
I can only prove part a
please help. thanks
(a) if its range on the horizontal plane is R, show that:
R^2sec^2θ -[2V^2R/g](tanθ)- [2hV^2/g] = 0
(b) without solving this equation, show that it has one negative root. Interpret the results.
(c) show that the maximum range for a given V is {V^2 + V[(V^2 +4hg)]^(1/2)}/2g, given the maximum range occurs when it is projected at θ = pi/4
2. (a) A particle is projected from ground level to just clear two walls of hiehgt 7m, and distant 7 metres and 14 metres from the point of projection. Prove that if θ is the angle of projection, then tanθ =3/2. Assume g = 10 m/s^2 and no air résistance
(b) Prove that if the walls are h metres high and distant b metres, and c metres from the pointof projection, then tanθ = h(b+c)/bc
I can only prove part a
please help. thanks