Answer:
a. Final velocity, V = 2.179 m/s.
b. Final velocity, V = 7.071 m/s.
Explanation:
<u>Given the following data;</u>
Acceleration = 0.500m/s²
a. To find the velocity of the boat after it has traveled 4.75 m
Since it started from rest, initial velocity is equal to 0m/s.
Now, we would use the third equation of motion to find the final velocity.
Where;
- V represents the final velocity measured in meter per seconds.
- U represents the initial velocity measured in meter per seconds.
- a represents acceleration measured in meters per seconds square.
- S represents the displacement measured in meters.
Substituting into the equation, we have;


Taking the square root, we have;

<em>Final velocity, V = 2.179 m/s.</em>
b. To find the velocity if the boat has traveled 50 m.


Taking the square root, we have;

<em>Final velocity, V = 7.071 m/s.</em>
Answer:
I = 2.19A, anticlockwise direction.
Explanation:
Given r = 33cm = 0.33m, N = 12, ΔB = 7.5 - 1.5 = 6.0T, Δt = 3s, R = 3.75Ω
By Faraday's law of electromagnetic induction when there is a change in flux in a coil or loop, an emf is induced in the coil or loop which is proportional to the time rate of change of the magnetic flux through the loop.
The emf E is related to the flux by the formula
E = – NdФ/dt
Where N = number of turns in the coil, Ф = magnetic flux through the loop = BA, B = magnetic field strength, A = Area
In this problem the strength of the magnetic field changes. As a result the flux too changes and an emf is induced in the coil.
So
ΔФ = ΔB×A = ΔB×πr² = 6×π×0.33² = 2.05Wb
E = -NΔФ/Δt = 12×2.05/3 = 8.2V
I = E/R = 8.2/ 3.75 = 2.19A
The direction of the current can be found by pointing the thumb of your right hand in the direction of the magnetic field and curling the remaining fingers around this direction. The direction of the curl of these fingers give the direction of current which in this case is anticlockwise.
Answer: 909 m/s
Explanation:
Given
Mass of the bullet, m1 = 0.05 kg
Mass of the wooden block, m2 = 5 kg
Final velocities of the block and bullet, v = 9 m/s
Initial velocity of the bullet v1 = ? m/s
From the question, we would notice that there is just an object (i.e the bullet) moving before the collision. Also, even after the collision between the bullet and wood, the bullet and the wood would move as one object. Thus, we would use the conservation of momentum to solve
m1v1 = (m1 + m2) v, on substituting, we have
0.05 * v1 = (0.05 + 5) * 9
0.05 * v1 = 5.05 * 9
0.05 * v1 = 45.45
v1 = 45.45 / 0.05
v1 = 909 m/s
Thus, the original velocity of the bullet was 909 m/s
Answer:
F = 64.0 N
the magnitude of the force is 64 N
Explanation:
Given;
Mass m = 45kg
time t = 7.5 s
Displacement d = 40 m
Force = mass × acceleration
F = ma ........1
From equation of motion;
d = vt + 0.5at^2
Since initial velocity v = 0 (initially at rest)
d = 0.5at^2
Making a the subject of formula;
a = d/(0.5t^2)
Substituting the given values;
a = 40/(0.5×7.5^2)
a = 1.42 m/s^2
From equation 1;
F = ma
Substituting the given values;
Force F = 45 kg × 1.42 m/s^2
F = 64.0 N
the magnitude of the force is 64 N