Question

A cannon fires a shell at 1500 m/s and 55-degrees. How long is it in the air? and how far did it go?

Answer 1

The time in the air and the distance a cannon shell travels can be calculated using projectile motion equations, factoring in the initial velocity and angle of launch.

Step-by-step explanation:

Calculating Projectile Motion Parameters

For the given problem where a cannon fires a shell at 1500 m/s and 55-degrees, we can calculate the time in the air and the distance it travels through projectile motion equations.

The time of flight (T) for a projectile launched at an angle θ with initial velocity v0 is given by:

T = (2 * v0 * sin(θ)) / g

, where g is the acceleration due to gravity (9.81 m/s

2

).

The horizontal range (R) can be calculated using the formula:

R = (v0

2

* sin(2 * θ)) / g

.

Let's calculate these for the given problem:

1. Calculate the vertical component of the initial velocity: v0y = v0 * sin(θ).
2. Calculate the time of flight: T = (2 * v0y) / g.
3. Calculate the horizontal component of the initial velocity: v0x = v0 * cos(θ).
4. Calculate the horizontal range: R = v0x * T.

By substituting the values, we can find the time the shell is in the air and the distance it traveled.