Question

An artillery shell is fired with an initial velocity of 300m/s at 55 degrees above the horizon. to clear an avalanche, it explodes on a mountainside 42.0 s after firing. what are the x and y coordinates of the shell where it explodes

Answer 1

To find the coordinates of where the shell explodes, we need to calculate the height at which it explodes and the horizontal displacement.

Step-by-step explanation:

To find the coordinates of where the shell explodes, we need to calculate the height at which it explodes and the horizontal displacement.

(a) To calculate the height, we need to find the vertical component of the velocity.

The initial velocity of the shell can be split into two components: the horizontal component (Vx) and the vertical component (Vy).

We can use the equation Vy = Voy + a * t, where Voy is the initial vertical component of the velocity, a is the acceleration (in this case 9.8 m/s^2) and t is the time (42.0 s).

Since the shell explodes at its highest point, the velocity at that point is 0 m/s. Solving for Voy, we get - a * t = Voy.

The height at which the shell explodes is then given by the equation h = h0 + Voy * t + 1/2 * a * t^2, where h0 is the initial height (which is 0 m).

(b) To calculate the time passed between the launch and explosion, we know that the shell explodes at its highest point, where the velocity is 0 m/s.

Using the equation Vy = Voy + a * t, we can solve for t.

(c) To calculate the horizontal displacement, we can use the equation x = Vx * t, where Vx is the initial horizontal component of the velocity.