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

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) = (1 km)/(5 s)*(1000 m)/(1 km) = 200 m/s`

Then, the acceleration is:

`a = (v_(f)^(2))/(2x) = ((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!