Question

Projectile motion! A plane in level flight is flying due east at 200 m/s. At a height of 3000m, an object is dropped (at point A). Take acceleration due to gravity to be 10 m/s/s downwards and ignore air resistance.

(a) Show that the Cartesian equation for the motion of the object is y = 3000 - x²/8000

(b) There is a dove hovering 5m below and 200m east of A. Use the Cartesian equation to find whether the object will hit the dove.

(TBC)

Answer 1

(c) The wingspanpit of a second plane in level flight travelling in the opposite direction towards the first plane, was at point B, 2500 m high and 5 km horizontally distant from the first plane, at the instant the object was released. At what speed must the second plane travel if the object is to strike the wingspanpit of the second plane?

Answer 2

ok for part a) you need x(t) and y(t) and then use substitution to obtain y(x).
x(t) = 200t , since plane is moving 200 m/s
y(t) = -(1/2)a*t^2 + initial height, a = 10, height = 3000
y(t) = 3000 - 5t^2

--> t = x/200
--> y = 3000 - 5(x/200)^2
--> y = 3000 - x^2/8000

part b) substitute 200 for x
--> y = 3000 - (200^2)/8000
--> y = 3000 - 5 = 2995
the object would have dropped 5m after traveling exactly 200m east, therefore hitting the dove

Answer 3

Thanks!!

Answer 4

nevermind,

plug in 2500 for y into equation to find x
--> 2500 = 3000 - x^2/8000
--> x^2/8000 = 500
--> x^2 = 4,000,000
--> x = 2000

remember, x = 200t
--> 200t = 2000
--> t = 10

plane is 5000m away and needs to be 2000m away, if they fly level, to catch object.
Therefore must fly 3000m in 10s
--> speed = 3000/10 = 300 m/s