A missile is fired horizontally with an initial velocity of 300 m/s from the top of a cliff 200.0 meters high.

a. How long does it take the missile to reach the bottom the cliff?

b. How far from the base of the cliff does the missile strike the ground?

h=gt²/2 => t=sqrt(2h/g)

L=vt=v• sqrt(2h/g)

To solve these problems, we need to use the equations of motion and the principles of projectile motion. Let's break it down step by step:

a. Finding the time of flight:
First, we need to find the time it takes for the missile to reach the bottom of the cliff.

We know that the initial velocity of the missile is 300 m/s, and it is fired horizontally. Since there is no vertical velocity initially, the only force acting on the missile in the vertical direction is the force of gravity.

Using the equation for vertical displacement under constant acceleration:

s = ut + (1/2)gt^2

Where:
s = vertical displacement (final position - initial position)
u = initial vertical velocity (0 m/s)
g = acceleration due to gravity (-9.8 m/s^2)
t = time

Since the missile starts from rest in the vertical direction, the initial vertical displacement is 200.0 meters, and the final vertical displacement is 0.

Therefore:

0 = (1/2)(-9.8)t^2

Rearranging the equation:

4.9t^2 = 200

Dividing both sides by 4.9:

t^2 = 200 / 4.9

Taking the square root of both sides:

t ≈ √(200 / 4.9)

Using a calculator, t ≈ 6.47 seconds (rounded to two decimal places).

Thus, it takes approximately 6.47 seconds for the missile to reach the bottom of the cliff.

b. Finding the horizontal distance traveled:
Since the missile is fired horizontally, there is no horizontal acceleration acting on it. The velocity in the horizontal direction remains constant throughout the motion.

Using the equation for horizontal distance:

s = vt

Where:
s = horizontal distance
v = horizontal velocity (300 m/s)
t = time (6.47 s)

Therefore:

s = 300 * 6.47

Using a calculator, s ≈ 1941 meters (rounded to two decimal places).

Therefore, the missile strikes the ground approximately 1941 meters from the base of the cliff.