Question

8. A projectile is fired from the origin in a straight line towards a rectangular target and hits it perpendicularly 2 seconds later. The vertices of the rectangle are (50,100,275), (100, 0, 275), (200,50, 150), and (150, 150, 150), where units are in meters. (a) At what point did the projectile hit the rectangle? (b) The projectile was trying to hit the center of the target. How accurate was it? (c) Assuming the projectile was moving at a constant speed, how fast was it moving? (d) The assumption in part (c) is not quite correct; in fact, the projectile was decelerating at a constant 5 m/s2 due to drag.2 What was the projectile's initial velocity? (Note: I am asking for velocity and not speed.)

Answer 1

Eqn of a plane is a(x - x_0) + b(y - y_0) + ((z - z_0) = 0 (a, b, c) is a vector normal to the plane (x_0, y_0, z_0) is a point on the plane consider any 3 points from the given A(50, 100, 275), B(100, 0, 278), C(200, 50, 150) = > V_1 = AB^bar = (100 - 50) i^^+ (0 - 100) j^^+ (275 - 275) k^^V_2 = BC^bar = (200 - 100) i^^+ (80 - 0) j^^+ (150 - 275) V_1 = 50 i^^- 100 j^^, V_2 = 100 i^^+ 50 j^^- 75 k^^V^bar_1 times V^bar_2 gives vector normal to plane = > Vertical-bar i^^50 100 j^^- 100 50 k^^0 - 75 Vertical-bar = i^^(75 times 100 - 50 times 0) - j^^(- 50 times 75 - 0 times 100) + k^^(50 times 50 + 100 times 100) = 7500 i^^+ 3750 j^^+ 12500 k^^ \r\n = > eqn of plane is 7500(x - 50) + 3750(y - 100) +