Physics Question?

Question

Physics question.?
"A terrorist, 800 metes from a take off point of a plane is about to hit the plane using a rocket launcher with a velocity of 280 meters per second inclined 30 degrees within the ground. If the plane has the take-off velocity of 100 meters per second at 15 degrees, how long will it take after the take-off before the rocket is fired in order to hit the target?show solution.

Answer 1

considering the motion of the plane to the impact point, the distance traveled along the ground is
cos(15)*100*t1
where t1 is the time of impact from the take-off of the plane
for the rocket
cos(30)*280*(t1-t2)
where t2 is the time lapse after plane take-off before rocket launch
Also, both distances must add to 800 m
so
800=cos(15)*100*t1+cos(30)*280*(t1-t2)
Also, the rocket and the plane must intersect at the same altitude for a strike. I will assume that gravity does not play a part in this since the plane and rocket both have engines. I will assume that they both travel at constant velocity and there is zero time acceleration.

sin(15)*100*t1 is the altitude of the plane
and
sin(30)*280*(t1-t2) is the altitude of the rocket
or
0=sin(15)*100*t1-sin(30)*280*(t1-t2)
solve the simultaneous equations for t2 and you have your answer.

t1=8/(cos(15)+sin(15)/tan(30))
and t2=4.61 seconds

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