A Canon shoots an artillery shell towards a target 4.54 km distant, where it lands at the same level it was shot. It was noted that the elapsed time of the projectile was 27.5 seconds. What was the muzzle velocity of the shell?

Question

A Canon shoots an artillery shell towards a target 4.54 km distant, where it lands at the same level it was shot. It was noted that the elapsed time of the projectile was 27.5 seconds. What was the muzzle velocity of the shell?

(there is a picture showing a canon shooting the muzzle over a mountain, but the angle was not given)

Answer 1

you know horizonal velocity (distance/time).

from time in air:
in the vertical component...
Vf=vi-4.9t^2
-vi*sinTheta=vi*sinTheta-4.9t^2, you know time inair, so solve for vi*sinTheta
a) vi*sinTheta=4.9*27.5^2/2

from horizonal velocity
b) vi*cosTheta=4.54/27.5

Now, divide a) by b) and you get an expression for
tanTheta= 4.9*27.5^2/2 / 4.54/27.5
and you can solve for Theta. From that, get Vi

Answer 2

To find the muzzle velocity of the shell, we can use the equations of motion for projectile motion. However, we need to know the angle at which the shell was fired in order to calculate accurately. Without the angle, we cannot determine the muzzle velocity.

If you have the angle at which the shell was fired, you can follow these steps to calculate the muzzle velocity:

1. Break down the initial velocity into its horizontal and vertical components. The horizontal component of velocity remains constant throughout the trajectory, while the vertical component is affected by gravity.

2. Use the vertical motion equation h = h0 + V0 * sinθ * t - (1/2) * g * t^2 to find the time of flight (t) of the shell. Here, h0 is the initial height, V0 is the initial vertical velocity (which is the muzzle velocity times the sin of the angle), g is the acceleration due to gravity (approximately 9.8 m/s^2), and h is the final height (which is zero in this case since the shell lands at the same level it was shot).

3. Once you have the time of flight (t), use the horizontal motion equation d = V0 * cosθ * t to find the horizontal distance traveled by the shell. Here, d is the horizontal distance, V0 is the muzzle velocity, θ is the launch angle, and t is the time of flight.

4. Plug in the given values of the horizontal distance (4.54 km or 4540 m) and the time of flight (27.5 s) into the equation from step 3, and solve for the muzzle velocity (V0).

However, since the angle of launch is not provided in the question, it is not possible to calculate the muzzle velocity with the information given.