Blake

Gandalf the Grey started in the Forest of Mirkwood at a point with coordinates(-1,2) and arrived in the Iron Hills at the point with coordinates(1, 5) . If he began walking in the direction of the vector v = 4i + 2j ,and changes direction only once, when he turns at a right angle, what are the coordinates of the point where he makes the turn.

consider a reservoir with a volume of 2 billion cubic meter and an initial pollutant concentration of .005g/m^3. There is a daily inflow of 100 million m^3 of water with a pollutant concentration of .0005g/m^3 and an equal daily outflow of the well-mixed water in the reservoir. How long will it take to reduce the pollutant concentration in the reservoir to .001 g/m^3.

A tank in the shape of an inverted right circular cone has height 12 meters and radius 7 meters. It is filled with 10 meters of hot chocolate.

Find the work required to empty the tank by pumping the hot chocolate over the top of the tank. Note: the density of hot chocolate is = 1470 kg/m^3

Ball bearings are made by letting spherical drops of molten metal fall inside a tall tower -- called a shot tower -- and solidify as they fall.

(a) If a bearing needs 4.0 s to solidify enough for impact, how high must the tower be?

(b) What is the bearing's impact velocity? (Take up to be positive.)

(a) What constant acceleration, in SI units, must a car have to go from zero to 56 mph in 9 s?

(b) What fraction of g is this?

(c) How far has the car traveled when it reaches 56 mph? Give your answer both in SI units and in feet.

Ball bearings are made by letting spherical drops of molten metal fall inside a tall tower -- called a shot tower -- and solidify as they fall.

(a) If a bearing needs 4.0 s to solidify enough for impact, how high must the tower be?

(b) What is the bearing's impact velocity? (Take up to be positive.)

You are driving to the grocery store at 22 m/s. You are 105 m from an intersection when the traffic light turns red. Assume that your reaction time is 0.50 s and that your car brakes with constant acceleration.

(a) How far are you from the intersection when you begin to apply the brakes?

(b) What acceleration (magnitude) will bring you to rest right at the intersection?

(c) How long (total) does it take you to stop?

A 1000 kg weather rocket is launched straight up. The rocket motor provides a constant acceleration for 18 s, then the motor stops. The rocket altitude 22 s after launch is 4700 m. You can ignore any effects of air resistance.

(a) What was the rocket's acceleration during the first 18 s?

(b) What is the rocket's speed as it passes through a cloud 4700 m above the ground?

A skier is gliding along at 2.5 m/s on horizontal, frictionless snow. He suddenly starts down a 16° incline. His speed at the bottom is 15 m/s. (a) What is the length of the incline?

(b) How long does it take him to reach the bottom?

a rock is tossed straight up with a speed of 18m/s. when it returns, it fallls int a hole of 12 m deep. a) what is the velocity of the rock as it hit the bottom of the hole? b)how long is the rock in the air, from the instant it is released until it hit the bottom of the hole?