The equation of motion of a missile is x = 3t, y = −4t, z = t, where time ‘t’ is in seconds and the distance is measured in kilometres.
If the position of the missile at a certain instant of time is (30, −40, 10), then what will be the height of the missile from the ground? (Ground is considered as the xy-plane.)
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → 10 km
The ground is the xy-plane, z = 0. The height above the xy-plane of a point (x, y, z) is its distance from that plane, which is |z|.
The point (30, −40, 10) is on the path: with t = 10,
\(x = 3\times 10 = 30,\quad y = -4\times 10 = -40,\quad z = 10\)
So the height of the missile is
\(z = 10\) km