One kind of slingshot consists of a pocket that holds a pebble and is whirled on a circle of radius r. The pebble is released fr
om the circle at the angle θ so that it will hit the target. The angle ϕ in the drawing is 37.1°. The distance to the target from the center of the circle is d. (See the drawing below, which is not to scale.) The circular path is parallel to the ground, and the target lies in the plane of the circle. The distance d is one times the radius r. Ignore the effect of gravity in pulling the stone downward after it is released and find the angle θ.
1 answer:
You might be interested in
Answer:
= 1,386 m / s
Explanation:
The mechanism behind rocket propulsion is defined by the formula
- v₀ =
ln (M₀ / Mf)
Here, v refers to the initial, final, and relative velocities, while M indicates the masses
The provided values include the relative velocity (see = 2000 m / s) and the initial mass, where the mass of the rocket when loaded is represented as (M₀ = 5Mf)
For our analysis, we assume the rocket begins at rest (v₀ = 0)
Once half of the fuel has burnt, the mass ratio indicates that the current mass is
M = 2.5 Mf
- 0 = 2000 ln (5Mf / 2.5 Mf) = 2000 ln 2
= 1,386 m / s
Answer:
The water level increases more when the cube is above the raft before it sinks.
Explanation:
The principle involved is based on Archimedes' theory, which states that immersing an object in water will raise the initial water level. This means that the height of the water in the container increases. The increase in water volume corresponds to the volume of the submerged object.
We can consider two scenarios: when the steel cube rests on the raft and when it settles at the pool's bottom.
When the cube rests at the pool’s bottom, the volume will indeed rise, and we can ascertain this using the cube's volume.
Vc = 0.45*0.45*0.45 = 0.0911 [m^3]
When an object floats, it's because the densities of the object and water are in equilibrium.
The formula for density is:
Ro = m/V
where:
m= mass [kg]
V = volume [m^3]
The buoyant force can be calculated with this equation:
Vs > Vc indicates that the combined volume of the raft and the cube exceeds that of the cube alone resting at the bottom of the pool. Hence, when the cube is positioned above the raft, the water level rises more before it becomes submerged.