Projectile motion (1 Viewer)

[cutemouse]

Hello,

I can do Part (i), just need help with he second part of part (ii) [show that k < 1+sqrt(2) .....] and part (iii)

Thanks

 

[untouchablecuz]

Hello,

I can do Part (i), just need help with he second part of part (ii) [show that k < 1+sqrt(2) .....] and part (iii)

Thanks

(i) solve the parametric equations simultaneously and you get the required equation

(ii) if the projectile hits the base of the target, then, x = a and y = a

sub these coordinates into the equation derived in part i) and you get the required equation

now, since this equation has roots that are conditions in which the projectile hits the base of the target (i.e satisfy x =a, y=a), the projectile will fall short of the target IF there are no real roots

i.e. discriminant < 0

find the discriminant and solve for k and you get [1-sqrt(2)] < k < [1+sqrt(2)], but since k is a positive constant, 0 < k < [1+sqrt(2)]

(iii) sub k = 3 into the equation derived in ii)

since k = 3 > [1 + sqrt(2)], the roots in tan(alpha) will form the endpoints at which the projectile will collide with the target

thus, solving for tan(alpha) we get tan(alpha) = 3 - sqrt(2) and tan(alpha) = 3 + sqrt(2)

tan(alpha) must be or lie between these two points and hence

3 - sqrt(2) <= tan(alpha) <= 3 + sqrt(2)