1 hectopascal (hPa) is equivalent to 100 Pa
Answer:
Part a)
Average EMF for half cycle is

Part b)
For one complete cycle we will have

Part c)
Maximum induced EMF will be at
t = 0.025 s and 0.075 s
minimum induced EMF is at
t = 0.05s and 0.1 s
Explanation:
As we know that magnetic field is oscillating in direction as well as magnitude
so induced EMF is given as

Part a)
For average value of EMF from positive maximum to negative maximum which is equal to half cycle
so we have




Part b)
For one complete cycle we will have


Part c)
Maximum induced EMF will be at

here we know

t = 0.025 s and 0.075 s
minimum induced EMF is at

so it is
t = 0.05s and 0.1 s
Answer:
3.88m/s
Explanation:
Using the law of conservation of momentum
m1u1+m2u2 = (m1+m2)v
m1 and m2 are the masses
u1 and 2 are the initial velocities
v is the final velocity
Given
m1 = 64kg
u1 = 4.2m/s
m2 = 25kg
u2 = 3.2m/s
Required
Final velocity v
Substitute the given values into the formula
64(4.2)+25(3.2) = (65+25)v
268.8+80 = 90v
348.8 = 90v
v = 348.8/90
v = 3.88m/s
Hence the velocity of the kayak after the swimmer jumps off is 3.88m/s
Formula for orbital speed, v = √(GM/R)
Where G is the universal gravitational constant, M = Central Mass,
R = Distance between centers of Mass.
Given. v = 68 m/s, M = ? , R = 410 km = 410000 m., G = 6.674 * 10⁻¹¹ Nm²/kg²
68 = √(GM/R)
68 = √(6.674 * 10⁻¹¹ * M/410000)
68² = (6.674 * 10⁻¹¹ * M)/410000
(68² * 410000) / 6.674 * 10⁻¹¹ = M
2.84 × 10¹⁹ = M
Mass of Planet Y = 2.84 × 10¹⁹ kg