Answer:
time taken.
Explanation:
F = ma
F = m × (v - u) / t
F = mv - mu / t
mv - mu = change in momentum
Answer:
a) 91 m/s
b) 111 m/s
Explanation:
v = u + at
v = 128sin60 + (-9.8)(2.0) = 91.25125... m/s
v = √(vx² + vy²) = √((128cos60)² + 91.25125²) = 111.4575... m/s
Answer:
The acceleration at the astronaut's head decreases.
Explanation:
Since the centripetal acceleration equals acceleration due to gravity,
a = g = GM/R². since a changes infinitesimally from his foot to his head, we differentiate a with respect to r to get da/dr = -2GM/R³.
So, da, the change in acceleration = -2GMdR/R³ = -2gdR/R = -2 × 9.8/6.4 × 10⁶ m = -3.0625 × 10⁻⁶dR m/s².
Since dR = height of astronaut = 1.80 m, da = -3.0625 × 10⁻⁶ × 1.8 = -5.5125 × 10⁻⁶ m/s².
So the acceleration at the astronaut's head is g + da = 9.8 - 0.0000055125 = 9.7999944875 m/s².
So the acceleration at the astronaut's head decreases.
Answer:
The frequency of the 4th harmonic of the string is 481.13 Hz.
Explanation:
When a stretch string fixed at both ends is set into vibration, it produces its lowest sound of possible note called the fundamental frequency. Under certain conditions on the string, higher frequencies called harmonics or overtones can be produced.
The frequency of the forth harmonic is the third overtone of the string and can be determined by:
f = 
Given that; L = 48.0 cm = 0.48 m,
m = 0.3 g = 0.0003 Kg,
T = 4.0 N,
f = 
f = 4.1667 × 115.4701
= 481.1252
f = 481.13 Hz
The frequency of the 4th harmonic of the string is 481.13 Hz.
Answer:
Impedance = 19.44ohms
Current = 5.14A
Power factor = 0.62
Explanation:
Impedance in an RLC AC circuit is defined as the total opposition to the flow of current in the resistor, inductor and capacitor.
Impedance Z = √R²+(Xl-Xc)²
Where R is the resistance = 12Ω
Inductance L = 0.15H
Capacitance C = 100uF = 100×10^-6F
Since Xl = 2πfL and Xc = 1/2πfC where f is the frequency.
Xl = 2π×50×0.15
Xl = 15πΩ
Xl = 47.12Ω
Xc = 1/2π×50×100×10^-6
Xc = 100/π Ω
Xc = 31.83Ω
Z =√12²+(47.12-31.83)²
Z = √144+233.78
Z = 19.44Ω
Impedance = 19.44ohms
To calculate the circuit current, we will use the expression V=IZ where V is the supply voltage = 100V
I = V/Z = 100/19.44
I = 5.14Amperes
To calculate the power factor,
Power factor = cos(theta) where;
theta = arctan(Xl-Xc)/R
theta = arctan(47.12-31.83)/12
theta = arctan(15.29/12)
theta = arctan1.27
theta = 51.78°
Power factor = cos51.78°
Power factor = 0.62
