You are trying to shoot supplies from the ground so that they reach the top of a

Question

You are trying to shoot supplies from the ground so that they reach the top of a plane while flying low. The plane is flying at an altitude of y=20 meters high and with a speed of 30m/s, and you want to project your medical supplies with an initial velocity of Vo=50m/s so that it follows the path described below (need to go up and down), at which angle (measure with respect to the ground) do you need to throw the medical supplies so that they don't miss the front of the plane, and how far away (distance d) does the plane need to be when you launch the supplies? To simplify the problem, replace the plane with point A.

Explanation / Answer

You are trying to shoot supplies from the ground so that they reach the top of a plane while flying low. The plane is flying at an altitude of y=20 meters high and with a speed of 30m/s, and you want to project your medical supplies with an initial velocity of Vo=50m/s so that it follows the path described below (need to go up and down), at which angle (measure with respect to the ground) do you need to throw the medical supplies so that they don't miss the front of the plane, and how far away (distance d) does the plane need to be when you launch the supplies? To simplify the problem, replace the plane with point A.

as per the situation of the problem at the maximum height of the medical supplies which should be 20m the horizontal distance should match with the chosen value

now let the supply be thrown at an angle

initial velocity =50m/sec

initial velocity in the horizontal direction=50cos

initial velocity wrt plane=30+50cos

as the supply is thrown from the front direction oppsite to the plane direction of motion.

initial velocity in the vertical direction=50sin

so maximum height =50*50 sin2/2g=20m=>=23.32degree.

horizontal distance=1/2(50*50sin2*23.32/g)=50.49m

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