Answer:
A. Vx = 3.63 m/s
B. Vy = -45.73 m/s
C. |V| = 45.87 m/s
D. θ = -85.46°
Explanation:
Given that position, r, is given as:
r = 3.63tˆi − 5.73t^2ˆj + 8.16ˆk
Velocity is the derivative of position, r:
V = dr/dt = 3.63 - 11.46t^j
A. x component of velocity, Vx = 3.63 m/s
B. y component of velocity, Vy = -11.46t
t = 3.99 secs,
Vy = - 11.46 * 3.99 = -45.73 m/s
C. Magnitude of velocity, |V| = √[(-45.73)² + 3.63²]
|V| = √(2091.2329 + 13.1769)
|V| = √(2104.4098)
|V| = 45.87 m/s
D. Angle of the velocity relative to the x axis, θ is given as:
tanθ = Vy/Vx
tanθ = -45.73/3.63
tanθ = -12.6
θ = -85.46°
Coffee mug is cylindrical shape. Therefore,
Volume of mug = volume of cylinder = πr²h
r = inner radius of mug. h = height of coffee = 6 cm.
Density of coffee = Density of water = 1 g/ml
Therefore, volume of coffee = mass/density = 400/1 = 400 ml = 400 cm³
Volume of coffee = πr²h
400= πr²(6)
r² = 21.23
r = inner radius of mug = 4.607 cm
Since the acceleration is uniform, we can calculate it from the data we are given:
a = (vf - vi)/2
where vf=33 m/s and vi=11 m/s
Then use Suvat's equation:
x(t) = vi*t + 0.5 * a * t
where t=20s
A catalyst is a substance that alters the reaction and doesn't involve in the reaction.So if the Manganese was a catalyst the mass would not have decreased,it would just continue aletring the reaction until its used up.
The Manganese is not acting as a catalyst
