1. ## Projectile motion.

First projectile motion question
. A ball was projected at an angle of xto the horizontal. One second later another ball was projected from the same point at an angle of yto the horizontal. One second after the second ball was released, the two balls collided. Find the speed of projection for the two balls.

Second projectile motion question. A projectile released with a velocity U m/s at an angle xto the horizontal, just clears two obstacles, both of height h m, whose distances from the point of projection are b m and 3b m respectively. Find the range of the projectile.

2. Originally Posted by totster
First projectile motion question

A ball was projected at an angle of x to the horizontal. One second later another ball was projected from the same point at an angle of y to the horizontal. One second after the second ball was released, the two balls collided. Find the speed of projection for the two balls.
Write out the equations of motion for the two projectiles and solve the set of equations at time t=0 corresponding to the two projectiles being in the same position.

The initial velocity of the first particle is:

$\displaystyle \dot{\bold{x}}_1(0)=\bold{v_1}=v_1(\cos(x),\sin(x) )$

and of the second:

$\displaystyle \dot{\bold{x}}_2(1)=\bold{v_2}=v_2(\cos(y),\sin(y) )$

The equations of motion are:

$\displaystyle \ddot{\bold{x}}_i = -g (0,1)\ \ \ \ \ i=1,2$

and the collision condition gives you:

$\displaystyle \bold{x}_1(2)=\bold{x}_2(2)$

CB