$[g=9\mathrm{.}8\frac{m}{s^2}$ and air resistance is neglected$]$ Assume that there is an object A thrown with an initial velocity $V_{1,i}=15\mathrm{.}0\frac{m}{s}$ making an angle ${}_1=50$ with the horizontal $($object $A$ is located at the origin of an $xy-$frame$).$ Assume you designed an interceptor device, that has a response time $t_0=0\mathrm{.}15s,$ which you place at a distance $d=30\mathrm{.}0m$ from the object A $.$ The interceptor will throw a projectile $B$ with a speed $V_{2,i}=25\mathrm{.}0\frac{m}{s}$ at unknown angle ${}_2.$ You need to determine whether the angle ${}_2$ exists. To do that you need to:

Find the condition$($s$)$ needed so that the interception would occur?

Determine whether projectile A will be intercepted or not? $[$note: graphical solution is not allowed$].$

a$.$ If the answer is that projectile A will be intercepted, then:

i$.$ Derive$/$write an equation that can be used to calculate the angle $[$in degrees$]$ that the initial velocity of projectile $B$ should have with respect to the $x-$axis? Draw a diagram showing the direction of the initial velocity and the interception trajectory?

ii$.$ Write down the equation needed to calculate the collision time? Then use the above parameters to calculate it$.$

iii. Write down the equations needed to calculate the coordinates of the interception point? Then use the above parameters to calculate those coordinates.