a cannonball is fired horizontally from the top of a cliff. the cannon is at height H=60.0m above ground level , and the ball is fired with initial horizontal speed v_0 .assume acceleration due to gravity to be g=9.80 find d/2 int terms of v_0

75m

To find the distance traveled by the cannonball horizontally (d/2) in terms of the initial horizontal speed (v_0), we need to use the equations of motion.

First, we need to find the time it takes for the cannonball to reach the ground. Since the cannonball is fired horizontally, its initial vertical velocity is 0. The only force acting on it vertically is gravity, causing it to fall downward. We can use the equation:

H = (1/2) * g * t^2

where H is the height (60.0m) and g is the acceleration due to gravity (9.80 m/s^2).

Rearranging the equation, we get:

t^2 = (2 * H) / g

Now, let's find the time it takes for the cannonball to hit the ground (t).

t = sqrt((2 * H) / g)

Once we know the time of flight, we can find the horizontal distance traveled (d) using the equation:

d = v_0 * t

where v_0 is the initial horizontal speed.

But we are asked to find d/2, so we can substitute this in the equation:

d/2 = (v_0 * t) / 2

Substituting the value of t we found earlier:

d/2 = (v_0 * sqrt((2 * H) / g)) / 2

Therefore, d/2 in terms of v_0 is:

d/2 = (v_0 * sqrt((2 * 60.0) / 9.80)) / 2

Simplifying this expression will give you the exact value of d/2 in terms of v_0.

45 m

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