A stone is aimed at a cliff of height h with an initial speed of v = 64.0 m/s directed 55.0° above the horizontal, as shown in the Figure below by the arrow. The stone strikes at A, 7.31 s after launching. What is the height of the cliff?

Question

A stone is aimed at a cliff of height h with an initial speed of v = 64.0 m/s directed 55.0° above the horizontal, as shown in the Figure below by the arrow. The stone strikes at A, 7.31 s after launching. What is the height of the cliff?

What is the maximum height H reached above the ground?

I have tried using this formula but something isn't right?
D=ViT + 1/2aT^2
D=(64)(7.31)+ (4.9)(7.31)^2
D=729.68m

Answer 1

To find the height of the cliff, you need to consider the vertical motion of the stone. The formula you used, D = V₀T + (1/2) aT², is only valid for linear motion. In this case, the stone is following a curved path due to gravity.

To solve for the height of the cliff, you can break down the motion of the stone into horizontal and vertical components. Let's assume the initial height of the stone is h₀, and the final position where it strikes the cliff is A.

1. Find the vertical component of the initial velocity:
V₀y = V₀ * sin(θ)
V₀y = 64 * sin(55°)

2. Find the time it takes for the stone to reach the cliff (A):
The time of flight can be calculated using the equation for vertical displacement:
h = h₀ + V₀y * T - (1/2) g * T²
Rearranging the equation and substituting known values:
0 = h₀ + V₀y * T - (1/2) g * T²

Since the stone reaches its final vertical position at A, the value of h becomes zero:
0 = h₀ + V₀y * T - (1/2) g * T²

Solving for T using this quadratic equation will give you the time taken for the stone to reach the cliff.

3. Once you have the time (T), you can substitute it back into the equation for vertical displacement to find the height of the cliff (h):
h = h₀ + V₀y * T - (1/2) g * T²

To find the maximum height (H) reached above the ground, you can use the equation for vertical displacement once again. This time, the initial height (h₀) is zero (since we're measuring from the ground), and the final vertical position where the stone reaches maximum height will be H:

H = h₀ + V₀y * T - (1/2) g * T²

Now you can use this information to solve for the height of the cliff (h) and the maximum height reached above the ground (H).

A stone is aimed at a cliff of height h with an initial speed of v = 64.0 m/s directed 55.0° above the horizontal, as shown in the Figure below by the arrow. The stone strikes at A, 7.31 s after launching. What is the height of the cliff?

hyu

To find the height of the cliff, you need to consider the vertical motion of the stone. The formula you used, D = V₀T + (1/2) aT², is only valid for linear motion. In this case, the stone is following a curved path due to gravity.