Question

A pyrotechnical expert needs to fire a 15 kg projectile from a launching device that has a barrel length of 2 meters. The projectile will need to be launched horizontally 1 km in 5 seconds. Calculate the force needed to launch the projectile.

Answer 1

Answer:

The force needed to launch the projectile is 150000 N.

Explanation:  

We can find the force using the following equation:

$F = ma$

Where:

m: is the mass = 15 kg

a: is the acceleration

First, we need to find the acceleration of the projectile:

$v_{f}^{2} = v_{0}^{2} + 2ax$                          

Where:

$v_{f}$: is the final speed

$v_{0}$: is the initial speed = 0

x: is the distance = 2 m

The final speed is:

$v_{f} = \frac{1 km}{5 s}*\frac{1000 m}{1 km} = 200 m/s$

Then, the acceleration is:

$a = \frac{v_{f}^{2}}{2x} = \frac{(200 m/s)^{2}}{2*2 m} = 10000 m/s^{2}$

Finally, the force is:

$F = ma = 15 kg*10000 m/s^{2} = 150000 N$

Therefore, the force needed to launch the projectile is 150000 N.

I hope it helps you!