Question

A 440 g model rocket is on a cart that is rolling to the right at a speed of 4.0 m/s. The rocket engine, when it is fired, exerts a 8.0 AND vertical thrust on the rocket. Your goal is to have the rocket pass through a small horizontal hoop that is 20 m above the launch point. At what horizontal distance left of the loop should you launch?

Answer 1

Answer:

x = 8.74m

Explanation:

Hello! Let's solve this!

Given a mass m = 0.44kg

v = 4m / s

F = 8N

y = 20m

Force on the rocket

F '= F * - (mg) = m * a

We cleared to

a = (F * (- mg)) / m = (F / m) * (- g)

The rocket will accelerate upwards at a time t given by x = v * t

We cleared t

t = x / v

From kinematics we have to

y = (1/2) * a * t2

We replace a and t

y = (1/2) * (F / m) * (- g) * (x / v) 2

We clear x that is the incognita.

$x=\sqrt{(2*y*v^{2} )/(F/m)-g}$

$x=\sqrt{(2*20m*(4)^{2} )/((8N/0.44kg)-9.8m/s^{2} )}$

x = 8.74m