Answer: The bottom of the ladder is moving at 3.464ft/sec
Explanation:
The question defines a right angle triangle. Therefore using pythagorean
h^2 + l^2 = 10^2 = 100 ...eq1
dh/dt = -2ft/sec
dl/ dt = ?
Taking derivatives of time in eq 1 on both sides
2hdh/dt + 2ldl/dt = 0 ....eq2
Putting l = 5ft in eq2
h^ + 5^2 = 100
h^2 = 25 = 100
h Sqrt(75)
h = 8.66 ft
Put h = 8.66ft in eq2
2 × 8.66 × (-2) + 2 ×5 dl/dt
dl/dt = 17.32 / 5
dl/dt = 3.464ft/sec
1. Answer: components
A two dimensional vector can be divided into two parts called horizontal component and vertical component.
A three dimensional vector can be divided into three components: one along x-axis, one along y-axis and one along z-axis.
Hence, the vector parts that add up to the resultant are called components.
2. Answer: 5 miles.
The resultant distance along the straight line from the starting point to the end point would be the displacement.
The displacement would be equal to the magnitude of the hypotenuse formed in the right triangle.
Displacement, 
3. Answer: Scalar
A scalar quantity has only magnitude. For example, speed and distance are scalar quantities and can be normally added to find the total.
A vector quantity has both magnitude as well as direction. The components are summed according to vector addition rules. For example, velocity, acceleration, force etc.
The electrical force between these two charges remains the
same. In coulomb’s law, it states that the magnitude of two charges (product of
two charges) is inversely proportional to the square of the distance. Since both
the magnitude and the distance are halved, therefore, the change in both quantities
will have no effect in the value of electrical force.
B. cart B
Explanation:
The acceleration of each cart is given by Newton's second law:


where F is the force applied, a is the acceleration and m is the cart's mass.
The force F applied is the same for the two carts, however the mass of cart A (mA) is twice than the mass of cart B (mB), so we can rewrite the two accelerations:


we see that the acceleration of cart B is twice the acceleration of cart A, therefore cart B will move faster and will win the race.
Answer:

Explanation:
Torque and energy of an electric dipole in an electric field we find: