A rock is thrown off a vertical cliff at an angle of 58.6o above horizontal. The cliff is 84.6 m high and the ground extends horizontally from the base. The initial speed of the rock is 21.8 m/s. Neglect air resistance.
To what maximum height, in meters, does the rock rise above the edge of the cliff?
vertical speed initial :(Vi): 21.8*sin58
initial KE in vertical: 1/2 m (21.8*sin58)^2
final change in potential energy:
mgh=1/2 m (21.8*sin58)^2
solve for height h above the upper edge of the cliff.
ok i got! what about these questions:
How high above the ground, in meters, is the rock 2.21 s before it hits the ground?
How far horizontally from the cliff, in meters, is the rock 2.21 s before it hits the ground?
using the same numbers given above
To find the maximum height the rock rises above the edge of the cliff, we need to analyze the projectile motion of the rock. Here's how you can calculate it:
1. Split the initial velocity into its horizontal and vertical components.
- The initial velocity of the rock is 21.8 m/s, and the angle of projection is 58.6 degrees above the horizontal.
- The horizontal component (Vx) remains constant throughout the motion, while the vertical component (Vy) changes due to gravity.
2. Calculate the initial vertical velocity (Vy).
- Vy = V × sin(theta)
- Vy = 21.8 m/s × sin(58.6o)
3. Calculate the time taken to reach maximum height.
- To reach the maximum height, the vertical velocity becomes zero, and the object starts descending. This happens halfway through the total time of flight.
- Use the equation: time of flight (t) = 2 × (Vy / g), where g is the acceleration due to gravity (9.8 m/s²).
- t = 2 × (Vy / g)
4. Calculate the maximum height (h).
- The maximum height is the displacement of the object in the vertical direction.
- Use the equation: h = Vy² / (2 × g)
Let's plug in the values and solve the calculations:
Vy = 21.8 m/s × sin(58.6o)
= 21.8 m/s × 0.8571 (rounded to 4 decimal places)
t = 2 × (Vy / g)
= 2 × (calculated Vy value / 9.8 m/s²)
h = (Vy²) / (2 × g)
= (calculated Vy value squared) / (2 × 9.8 m/s²)
Solving these equations will give you the maximum height the rock rises above the edge of the cliff.