Mathematics Integration Level: Misc Level
A conical vessel whose height is 4 meters and the base radius 2 meters is being filled with water at the rate of 0.75 cubic meters per minute. Find the rate at which the level of the water is rising when the depth of water is 1.5 meters.
Mathematics Integration Level: Misc Level
Sand is pouring from a pipe at the rate of 12 cm3/sec. The falling sand forms a cone on the ground in such a way that the height of is always one-sixth of the radius of the base. How fast is the height of the sand cone increasing when the height is 4 cm?
Mathematics Integration Level: Misc Level
A circular cone with semi-vertical angle 45o, is fixed with its axis vertical an its vertex downwards. Water is poured into the cone at the rate of 2 cm3 per second. Find the rate at which the depth of the water id increasing when the depth is 4 cm.
Mathematics Integration Level: Misc Level
A kite is 120 m high and 130 m of string is out. If the kite is moving horizontally at the rate of 5.2 m/sec, find the rate at which the string is being paid out at that instant.
Mathematics Integration Level: Misc Level
A girl of height 1.6 m walks at the rate of 50 meters per minute away from a lamp which is 4 m above the ground. How fast is the girl's shadow lengthening?
Mathematics Integration Level: Misc Level
The top of a ladder 6 meters long is resting against a vertical wall. Suddenly, the ladder begins to slide downwards. At the instant when the foot of the ladder is 4 meters from the wall, it is sliding away at the rate of 0.5 m/sec. How fast is the top sliding downwards at this moment? How far is the foot from the wall when the foot and the top are moving at the same rate?
Mathematics Integration Level: Misc Level
The length x of a rectangle is decreasing at the rate of 5 cm/minute and the width y is increasing at the rate of 4 cm/minute. When x=8 cm, find the rate of change of
(i) the perimeter
(ii) the area of the rectangle
Mathematics Integration Level: Misc Level
A stone is dropped into a quiet lake and waves move in circles at a speed of 4 cm/sec. At the instant when the radius of the circular wave is 10 cm, how fast is the enclosed area increasing?
Mathematics Integration Level: Misc Level
Find the rate of change of the whole surface of a closed cylinder of radius r and height h with respect to change in radius.
Mathematics Integration Level: Misc Level
Find the rate of change of area of a circle of radius r with regard to its radius. How fast is the area changing with respect to the radius when the radius is 5 cm?
Physics Gravitation Level: Misc Level
2-The earth,s moon has a radius of 1.76x10^6 m and a mass of 7.35 x10^22 kg.
A-Calculate the acceleration due to gravity (g)on the moon.
B-How long would it take for a mass of 1 kg to fall a distance of 2 m to the surface of the moon?
G=6.673X10^-11 Nm2/kg2
Physics Force & Laws Of Motion Level: Misc Level
1-A block of mass m is at rest lying on the face of an incline plane. The plane makes an angle with the horizontal.
A- Draw the free body diagram showing all the forces acting on the block.
B- Write the equations for the net forces acting on the block. Be sure to specify your choice and coordinate system.
Physics Magnetism,Magnetic Effects Of Current Level: Misc Level
Determine the magnitude of the magnetic field midway between two long straight wires 0.6 cm apart in terms of the current 1.0 E1 A in one when the other carries 2.0 E1 A. Assume that the currents are in the same direction.
Determine the magnitude of the magnetic field midway between two long straight wires 0.6 cm aspart in terms of the current 1.0 E1 A in one when the other carries 2.0 E1 A. Assume that the currents are in the opposite direction.
Physics Modern Physics Level: Misc Level
A straight stream of protons a given point in space at a rate of 1.2 E9 proton /s. What magnetic field do they produce 1.3 m from the beam?
Physics Magnetism,Magnetic Effects Of Current Level: Misc Level
A power line carries a current of 92 A along the tops of 9.3-m - high poles.
What is the magnitude of the magnetic field produced by this wire at the ground?
How does this compare with the Earth,s field of about 1/2 G?
The Field of the cable is about ---% that of the Earth.
