A cannon tilted up at a 30 angle fires a cannon ball at 80 m/s from atop a 10-m-high fortress wall. what is the ball's impact speed on the ground below?

To find the velocity of the bullet just before reaching the ground, we use the formula.

Vy = Vosen (30 °) + gt (1).

For that we need to know the time it takes for the bullet to reach the ground from the moment it is fired.

For that we use the formula:

Xy = Xo + Vosen (30 °) * t + 0.5gt ^ 2 (2)

where:

Vy = Component of the speed in the y direction (vertical)

Vo = initial velocity of the bullet at the exit of the cannon

g = acceleration of gravity

Xy = vertical component of the position.

Xo = initial position.

t = time.

To find the time it takes for the bullet to reach the ground, we make Xy = 0 and clear t.

then it would be:

0 = 10 + 80sen (30 °) * t + 0.5 * ( - 9.8) t ^ 2.

The solution to that equation is:

t = 8.4 seconds.

We substitute that time in equation (1) and clear Vy.

We have left:

Vy = 80 * sin (30 °) + 9.8 * (8.4)

Vy = 42.38 m / s