Pearl is 54 5/6 inches tall. Lucas is 1 1/3 inches shorter than Pearl and Jane is 1 1/4 inches shorter than Lucas. How tall is Jane?

52 1/4

Step-by-step explanation:

1. A) A 10 kg dog running down the street at 30 mph

Momentum is defined as the product between mass (m) and velocity (v):

The momentum of the four objects is:

A) dog:

B) the walker is walking slowly, so its velocity is small and its momentum is small.

C) Bullet:

D) The truck is at rest, so v=0 and p=0

2. B) A tightrope walker crossing Niagara Falls

Gravitational potential energy is the product between mass (m), gravitational acceleration (g) and height (h)

the walker in Niagara Falls has for sure the greatest potential energy, since he is located at a very great height (h) compared to the other objects.

3. C) a 0.02 kg bullet moving down the barrel at 800 mph

Kinetic energy is:

where v is the speed of the object. We see that K depends on the square the speed: larger speed means larger kinetic energy, so the bullet has the greatest kinetic energy since it has largest speed.

4. D) A semi-truck parked in a parking lot

Inertia is the resistance of an object to any change in its motion. It depends only on the mass of the object. The greater the mass, the larger the inertia. The truck has the largest mass, so it also has the largest inertia.

5. b) 75 J

The work done is equal to the product between the force applied and the distance through which the object has been moved, in this case it is equal to:

6. a) 75 J

The potential energy gained by an object of weight W when lifted by a height h is given by:

In this case, W=50 N and h=1.5 m, so the gain in potential energy is

7. a) Object A

The acceleration of each mass along the ramp is:

where is the angle of the ramp. The time t taken to reach the bottom of the ramp of length L is given by:

(1)

the length of the two ramps is different, because they have same height h but different stepness. The length of the ramp, L, is

Substituting into (1)

the larger the angle, the smaller the time taken to reach the bottom of the ramp: so, object A (which is on a the steeper ramp) takes less time to reach the bottom.

8. c) Neither - they have same speed

We can use the conservation of energy: the initial potential energy of each box, U, is equal to the final kinetic energy, K:

so, we see that the final speed of each box (v) depends only on the initial height (h), which is the same for the two boxes (3 m), so they reach the bottom with the same speed.

9. b) cart B

The acceleration of each cart is given by Newton's second law:

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 the two accelerations will be:

so, 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.

10. c) Neither- they have same KE

We can apply the work-energy theorem: the work done on each cart is equal to its gain in kinetic energy:

we can neglect the initial kinetic energy, since the two carts start from same speed:

The work done is the product between the force F and the distance d:

the two children apply same force F over the same distance d, so the work done is the same, and the two carts have same final kinetic energy.

11a. 12.75 J

The work done is the product between the force applied (F=15 N) and the distance covered (d=85 cm=0.85 m):

11b. 10.63 N

The work done is:

(1)

to reach the same height h as before, the work done must be the same:

(2)

The distance is d=120 cm=1.20 m, so we can combine (1) and (2) to find F:

12a. Chemical energy into thermal energy

In a burning candle, the wax is burned together with oxygen to form heat. The initial form of energy is chemical energy (the energy stored in the chemical bonds of the wax and the oxygen), while the final form of energy is thermal energy (heat, which is energy due to the random motion of the molecules, which is greater if the temperature of the substance is greater)

12b. Electrical energy into thermal energy and radiation

Electrical current pass through the light bulb and it is converted into heat and light. The initial form of energy is electrical energy (due to the electrical current), while the final forms of energy are thermal energy (the heat) and radiation (related to the light emitted by the bulb)