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?

see below:

http://www.jiskha.com/display.cgi?id=1386888436#1386888436.1386888818

To solve this problem, we can use the equations of motion. Let's consider the motion in the horizontal and vertical directions separately.

a. How long does it take the missile to reach the bottom of the cliff?
To find the time it takes for the missile to reach the bottom of the cliff, we need to focus on the vertical motion. We can use the equation for vertical motion:

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

Where:
h = height (200.0 meters)
u = initial vertical velocity (0 m/s since the missile is fired horizontally)
t = time taken
g = acceleration due to gravity (approximately 9.8 m/s^2)

Since the missile is fired horizontally, its initial vertical velocity is zero. Therefore, the equation simplifies to:

h = (1/2)gt^2

Plugging in the values, we get:

200.0 = (1/2)(9.8)t^2

Rearranging the equation, we find:

t^2 = (2 * 200.0) / 9.8

t^2 ≈ 40.82

Taking the square root of both sides, we find:

t ≈ 6.38 s

Therefore, it takes approximately 6.38 seconds for the missile to reach the bottom of the cliff.

b. How far from the base of the cliff does the missile strike the ground?
To find the horizontal distance traveled by the missile, we can use the equation for horizontal motion:

d = u * t

Where:
d = horizontal distance
u = initial horizontal velocity (300 m/s)
t = time taken (6.38 s)

Plugging in the values, we get:

d = 300 * 6.38

d ≈ 1914.0 meters

Therefore, the missile strikes the ground approximately 1914.0 meters away from the base of the cliff.