A 3500-pF air-gap capacitor is connected to a 25-V battery. If a piece of mica is placed between the plates, how much charge will flow from the battery?

On a trip, you get stuck in slow traffic and have to drive 90.0 km at 30.0 km/hr. Then the traffic clears up, and you're able to drive another 90.0 km at 60.0 km/hr.

a) Calculate your overall average speed for this 180.0 km trip. Check: it's not 45.0 km/hr! See the next question as well. Use the definition of average speed in physics.

b) Prove that if you'd driven 180. km at 60.0 km/hr for the second leg, your overall average speed would have been 45.0 km/hr.

c) In the original description of the trip, why was your overall average speed lower than 45.0 km/hr, the mathematical average of 30.0 km/hr and 60.0 km/hr?

d) Determine the speed at which you'd have to have driven the second 90.0 km so that your overall average speed would have been 45.0 km/hr.

e) What are the largest and smallest possible average velocities for this trip, as originally described? What further information would allow you to determine where in this range your actual average velocity was? Explain in practical terms.

A car is parked on a cliff overlooking the ocean on an incline that makes an angle of 25.0° below the horizontal. The negligent driver leaves the car in neutral, and the emergency brakes are defective. The car rolls from rest down the incline with a constant acceleration of 3.97 m/s2 for a distance of 55.0 m to the edge of the cliff, which is 40.0 m above the ocean. (a) Find the car's position relative to the base of the cliff when the car lands in the ocean. m (b) Find the length of time the car is in the air. s

please answer and show your work, thank you!

1.) A farsighted person has a near point that is 48.0 cm from her eyes. She wears eyeglasses that are designed to enable her to read a newspaper held at a distance of 27.0 cm from her eyes. Find the focal length of the eyeglasses, assuming each of the following.

(a) that they are worn 2.0 cm from the eyes
cm

(b) that they are worn 3.0 cm from the eyes
cm

2.) A converging lens (f = 11.4 cm) is located 33.0 cm to the left of a diverging lens (f = -6.06 cm). A postage stamp is placed 39.6 cm to the left of the converging lens.

(a) Locate the final image of the stamp relative to the diverging lens. (Include sign to indicate which side of the lens the image is on.)
____________cm

(b) Find the overall magnification.
________________

3.) The owner of a van installs a rear-window lens that has a focal length of -0.301 m. When the owner looks out through the lens at a person standing directly behind the van, the person appears to be just 0.237 m from the back of the van, and appears to be 0.335 m tall.

(a) How far from the van is the person actually standing?
___________m

(b) How tall is the person?
___________m

A closed and elevated vertical cylindrical tank with diameter 2.00m contains water to a depth of 0.900m . A worker accidently pokes a circular hole with diameter 0.0190m in the bottom of the tank. As the water drains from the tank, compressed air above the water in the tank maintains a gauge pressure of5.00�103Pa at the surface of the water. Ignore any effects of viscosity.

A. Just after the hole is made, what is the speed of the water as it emerges from the hole? in m/s

B. What is the ratio of this speed to the efflux speed if the top of the tank is open to the air?

C. How much time does it take for all the water to drain from the tank? in min

D. What is the ratio of this time to the time it takes for the tank to drain if the top of the tank is open to the air?

Please help I have no idea how to solve it

Q1

Five capacitors are connected across a potential difference Vab as shown in Figure. Because of the dielectrics used, each capacitor will break down if the potential across it is V=61 V. What should be the value of Vab (with one decimal place) if you reach the break down voltage one of the capacitor.

Q2
Suppose after charging a 3.7

a) What is the difference between Beam-Width and First Null Beam-Width?

b) A 70% efficient antenna is having a radiation resistance (Rr) and loss resistance (RL). Calculate the ratio between (Rr) and (RL).

c) Calculate the maximum effective aperture of an antenna operating at a wavelength of 0.5m and has a directivity of 250.

In each of the following situations, Emma is in the exact center of a glass-sided freight car speeding to the right at a very high speed v relative to you. For each question, explain your reasoning.

1. Emma has a flashlight in each hand and directs them at the front and rear ends of the freight car. She then switches the flashlights on at the same time.

   1. In Emma

A 2 kg block is dragged up a hill at an acceleration of 1.8. If the hill is inclined at 30 and the coefficient of friction is 0.1 what force must be applied?

I got 15.2 but it was marked wrong

no other info

A 100 kg ball has a force acting on it. This force is: F(t) =.4ti -.7tj

when t = 0 seconds then x = 0 meters

initial velocity: v = 3i - 2j

Question: How do you find velocity and displacement the at 4 seconds?

I am not sure how to apply integration to this problem. Please show step by step how to solve.

A metal cylinder of mass ? = 5 kg with a coaxial hole is sliding horizontally on a metal rod. A spring with spring constant ? = 500 N/m is attached to the cylinder. The other end of the spring is attached on a table at a vertical distance of ℎ = 0.3 m below the cylinder. The spring has an equilibrium length of ?_0 = 0.5 m.

a) What is the horizontal position ?0 of the cylinder when the spring is at its natural equilibrium length of ?0 = 0.5 m? Define the attachment point of the spring on the table as position ? = 0.

b) What is the length ? of the spring when the cylinder is at any given position ??

c) Draw a free-body diagram of the cylinder.

d) Show that the horizontal force from the spring on the cylinder is: ?? = −?? (1 − ?0 √? 2 + ℎ 2 )