Respuesta :
Answer:
The distance from the base of the bookcase the bucket should be placed is approximately 2.444 meters
Explanation:
The given parameters are;
The speed with which the marble was launch, u = 3 m/s
The direction in which the marble was launched = 25 degrees
The height of the launcher above the ground, h = 1.3 m
The time it takes the marble to reach maximum height, [tex]t_{max}[/tex], is given as follows;
v × sinθ = g × [tex]t_{max}[/tex]
[tex]t_{max}[/tex] = v × sinθ/(g) = 3×sin(25)/9.81 ≈ 0.192 seconds
The time back to the top of the bookshelf level = The time to maximum height ≈ 0.192 seconds
The time it takes the marble to reach the from top of the bookshelf level is given by the equation for free fall using the vertical component of the velocity as follows;
h = 1/2×g×t²
1.3 = 1/2 × 9.81 × t²
t² = 1.3/(1/2 × 9.81) ≈ 0.265 s²
t ≈ 0.515 seconds
Total time of flight of the marble = 0.192 seconds + 0.192 seconds + 0.515 seconds ≈ 0.899 seconds
The distance from the base of the bookcase the bucket should be placed = The total horizontal range of the marble
The total horizontal range of the marble = The horizontal component of the velocity × Time of flight of the marble
∴ The total horizontal range of the marble = u × cos(θ) × [tex]t_{(Time \ of \ flight)}[/tex] = 3 × cos(25) × 0.899 ≈ 2.444 meters
∴ The distance from the base of the bookcase the bucket should be placed ≈ 2.444 meters.
