a ball is thrown inclined in to the air with a initial velocity of u. if it reaches the maximum height in 6 seconds , find the r
1 answer:
You might be interested in
Answer:
θ = 13.7º
Explanation:
- According to the work-energy theorem, the change in the kinetic energy of the combined mass of the child and the sled, is equal to the total work done on the object by external forces.
- The external forces capable to do work on the combination of child +sled, are the friction force (opposing to the displacement), and the component of the weight parallel to the slide.
- As this last work is just equal to the change in the gravitational potential energy (with opposite sign) , we can write the following equation:
- ΔK, is the change in kinetic energy, as follows:
- ΔU, is the change in the gravitational potential energy.
- If we choose as our zero reference level, the bottom of the slope, the change in gravitational potential energy will be as follows:
- Finally, the work done for non-conservative forces, is the work done by the friction force, along the slope, as follows:
- Replacing (2), (3), and (4) in (1), simplifying common terms, and rearranging, we have:
- Replacing by the givens and the knowns, we can solve for sin θ, as follows:
⇒ θ = sin⁻¹ (0.236) = 13.7º
Answer:
θ = 30°
Explanation:
Firts, the angle when the beam of light passes through the block cam be calculated using Snell Law:
<u>Where</u>:
n₁: is the index of refraction of the incident medium (air) = 1
θ₁: is the incident angle = 30°
n₂: is the medium 2 (plastic) = 1.46
θ₂: is the transmission angle
Hence, θ₂ is:
Now, when the beam of light re-emerges from the opposite side, we have:
n₁: is the index of refraction of the incident medium (plastic) = 1.46
θ₁: is the incident angle = 20.03°
n₂: is the medium 2 (air) = 1
θ₂: is the transmission angle
Hence, the angle to the normal to that surface (θ₂) is:
Therefore, we have that the beam of light will come out at the same angle of when it went in, since, it goes from air and enters to a plastic medium and then enters again in this medium to go out to air again. This was proved using the Snell Law.
I hope it helps you!