A ball is thrown from the ground toward a cliff of height h with a speed of 30.0 m/s and an angle of 60o

above horizontal. It lands on the cliff 4.00 s later. How high is the cliff?

Answer: 25.5 m

But having difficulty getting this answer

u = 30 cos 60 = 15 m/s

so x = 15 * 4 = 60 meters away if we are interested

now vertical
Vi = 30 sin 60 = 26 m/s
how far up in 4 seconds?
h = Vi t - 4.9 t^2
= 26(4) - 4.9(16)
= 104 - 78.4
= 25.6 I get, wonder if you use 4.9 for 9.81/2

To find the height of the cliff, we need to break down the vertical and horizontal components of the motion of the ball.

Step 1: Calculate the vertical component of the initial velocity.
The initial velocity of the ball can be broken down into horizontal and vertical components. The vertical component can be calculated using the formula:
Vertical component of initial velocity (Vy) = initial velocity (V) * sin(angle)
Here, the angle is 60 degrees and the initial velocity is 30.0 m/s.
Vy = 30.0 m/s * sin(60°)

Step 2: Calculate the time it takes for the ball to reach the maximum height.
When the ball reaches the maximum height, its vertical velocity becomes zero. We can use this fact to determine the time it takes to reach the maximum height. We can use the following formula to find the time:
Time to reach maximum height (t) = Vy / g
Here, g is the acceleration due to gravity, which is approximately 9.8 m/s^2.

Step 3: Calculate the maximum height.
The maximum height can be found using the formula for vertical displacement in free fall motion:
Vertical displacement (h) = Vy * t - (1/2) * g * t^2

Step 4: Calculate the time it takes for the ball to land on the cliff.
Given in the question, the total time taken for the ball to land on the cliff is 4.00 s.

Step 5: Calculate the vertical displacement.
The vertical displacement for the ball's downward motion can be calculated using the formula:
Vertical displacement (h) = Vy * t + (1/2) * g * t^2

Step 6: Calculate the height of the cliff.
The height of the cliff is the sum of the maximum height and the vertical displacement for the ball's downward motion.

Now, let's calculate the answer step by step:

1. Calculate the vertical component of the initial velocity:
Vy = 30.0 m/s * sin(60°) = 25.98 m/s

2. Calculate the time it takes to reach the maximum height:
t = Vy / g = 25.98 m/s / 9.8 m/s^2 = 2.653 s

3. Calculate the maximum height:
h = Vy * t - (1/2) * g * t^2
= 25.98 m/s * 2.653 s - (1/2) * 9.8 m/s^2 * (2.653 s)^2
= 68.92994 - 64.74867
= 4.18127 m

4. Calculate the vertical displacement for the ball's downward motion:
Vertical displacement (h) = Vy * t + (1/2) * g * t^2
= 25.98 m/s * 4 s + (1/2) * 9.8 m/s^2 * (4 s)^2
= 103.92 + 78.4
= 182.32 m

5. Calculate the height of the cliff:
height of the cliff = maximum height + vertical displacement
= 4.18127 m + 182.32 m
= 186.501 m

Therefore, the height of the cliff is approximately 186.501 meters according to the calculations. However, the given answer is 25.5 m. To obtain this answer, additional information or clarification may be needed.