Answer:
6.03 mV
Explanation:
length of solenoid, L = 2 m, N = 12000, di/dt = 40 A/s,
Magnetic field due to solenoid
B = μ0 n i = μ0 N i / L
dB/dt = μ0 N / L x di / dt
dB /dt = (4 x 3.14 x 10^-7 x 12000 x 40) / 2 = 0.3 T/s
Induced emf, e = rate of change of magnetic flux
e = dΦ / dt = A x dB / dt
e = 3.14 x 0.08 x 0.08 x 0.3 = 6.03 x 10^-3 V = 6.03 mV
Range of a projectile motion is given by
R = v cos θ / g (v sin θ + sqrt(v^2 sin^2 θ + 2gy_0)); where R = 188m, θ = 41°, g = 9.8m/s^2, y_0 = 0.9
188 = v cos 41° / 9.8 (v sin 41° + sqrt(v^2 sin^2 41° + 2 x 9.8 x 0.9)) = 0.07701(0.6561v + sqrt(0.4304 v^2 + 17.64)) = 0.05053v + 0.07701sqrt(0.4304v^2 + 17.64)
0.07701sqrt(0.4304v^2 + 17.64) = 188 - 0.05053v
0.005931(0.4304v^2 + 17.64) = 35344 - 19v + 0.002553v^2
0.002553v^2 + 0.1046 = 35344 - 19v + 0.002553v^2
19v = 35344 - 0.1046 = 35343.8954
v = 35343.8954/19 = 1860 m/s
Answer:
A + B = C Ax = 2 Ay = 0 Bx = 0 By = 6
Ax + Bx = Cx = 2
Ay + By = Cy = 6
C = (2^2 + 6^2)^1/2 = 6.32
Tan Cy / Cx = 6 / 2 = 3
Cy at 71.6 deg
Answer:
a) -2.038 m/s²
b) 40.33 mph
c) 312.5 m
Explanation:
t = Time taken
u = Initial velocity
v = Final velocity
s = Displacement
a = Acceleration
Acceleration of the boat is -2.083 m/s² if the boat will stop at 150 m.
Speed of the boat by when it will hit the dock is 18.03 m/s
Converting to mph
Speed of the boat by when it will hit the dock is 40.33 mph
The distance at which the boat will have to start decelerating is 312.5 m
