As a science fair project, you want to launch an 950g model rocket straight up and hit a horizontally moving target as it passes 40.0m above the launch point. The rocket engine provides a constant thrust of 18.3N . The target is approaching at a speed of 19.0m/s . At what horizontal distance between the target and the rocket should you launch?

55.28 m

Explanation:

Mass of the rocket = 950 g = 950 / 1000 = 0.95 kg

force of gravity = 0.95 Kg × 9.81 m/s² = 9.3195 N

force due to acceleration = 18.3 N - 9.3195 N = 8.9805 N

F = ma

acceleration of the rocket = F / m = 8.9805 N / 0.95 Kg = 9.45 m/s²

using the equation of motion

d = ut + 1/2 at² u = 0 m/s

d = 1/2 at²

t = √(2d / a) = √ ( 2 × 40 m /  9.45 m/s²) = 2.91 s

the horizontal distance between the target and the rocket = vt = 19 m/s × 2.91 s = 55.28 m