An object is thrown straight down off of a cliff with a velocity of 18m/s.

a) What is the object's velocity after 15s?
b) If the cliff is 358m high, how long does it take for the object to hit the ground?

Assuming acceleration is the force of gravity.

Vf = Vi + a*t
Vf = 18m/s + 9.81ms^-2 * 15s
Vf = 165.15 m/s

d = Vi*t + 1/2a*t^2
358 = 18m's*t + (1/2)9.81ms^-2 * t^2
Set it to zero:
0 = 4.91ms^-2 * t^2 + 18m/s * t - 358.
Use quadratic formula

t = 6.9s or t = -10.5s

Can't have negative time. Therefore it takes 6.9 seconds.

To answer part a):

We know that the object is being thrown straight down off of a cliff, so we can assume that the acceleration due to gravity is acting in the downward direction. This means that the object's velocity will increase due to gravity.

We can use the equation for velocity to calculate the object's velocity after a certain time:

v = u + at

Where:
v = final velocity (unknown)
u = initial velocity (given as 18 m/s)
a = acceleration (we'll assume it's -9.8 m/s^2 because it's acting in the downward direction)
t = time (given as 15 s)

Plugging in the values into the equation:

v = 18 m/s + (-9.8 m/s^2) * 15 s

After calculating, you'll find that the object's velocity after 15s is -132 m/s. The negative sign indicates that the object is moving downward.

Now let's move on to part b):

To find out how long it takes for the object to hit the ground, we can use the equation for displacement:

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

Where:
s = displacement (358 m, since that's the height of the cliff)
u = initial velocity (given as 18 m/s)
a = acceleration (again, -9.8 m/s^2)
t = time (unknown)

Plugging in the values, we get:

358 m = 18 m/s * t + (1/2) * (-9.8 m/s^2) * t^2

This is a quadratic equation in terms of t. Solving it will give you two possible values for t: one positive and one negative. Since time cannot be negative, we can discard the negative value.

By solving the quadratic equation, you'll find that it takes approximately 8.62 seconds for the object to hit the ground.

So, the answers are:
a) The object's velocity after 15s is -132 m/s.
b) It takes approximately 8.62 seconds for the object to hit the ground.