Mechanics: Motion in a plane, force, energy.

1. A river flows due east at 1.00 m/s. A boat crosses the river from the south shore to the north shore by maintaining a constant velocity of 9.0 m/s due north relative to the water.
(a) What is the velocity of the boat relative to shore?
(b) If the river is 280 m wide, how far downstream has the boat moved by the time it reaches the north shore?

2. A Chinook Salmon has a maximum underwater speed of 3.58 m/s, but it can jump out of water with a speed of 6.37 m/s. to move upstream past a waterfall, the salmon does not need to jump to the top of the fall, but only to a point in the fall where the water speed is less than 3.58 m/s; it can then swim up the fall for the remaining distance. Because the salmon must make forward progress in the water, let's assume that it can swim to the top if the water speed is 3.00 m/s. If water has a speed of 1.65 m/s as it passes over a ledge, how far below the ledge will the water be moving with a speed of 3.00 m/s? If the salmon is able to jump vertically upward from the base of the fall, what is the maximum height of waterfall that the salmon can clear?

3. A person sees a lightning bolt pass close to an airplane that is flying in the distance. The person hears thunder 7.0 s after seeing the bolt and sees the airplane overhead 14 s after hearing the thunder. The speed of sound in air is 1100 ft/s.
(a) Find the distance of the airplane from the person at the instant of the bolt. (Neglect the time it takes the light to travel from the bolt to the eye.)
(b) Assuming that the plane travels with a constant speed toward the person, find the velocity of the airplane.
(c) Look up the speed of light in air, and defend the approximation used in (a).

4. A 2.00 kg block situated on a rough incline is connected to a spring of negligible mass having a spring constant of 100 N/m (Fig. P5.76). The block is released from rest when the spring is unstretched, and the pulley is frictionless. The block moves 17.4 cm down the incline before coming to rest. Find the coefficient of kinetic friction between the block and incline.

5. (a) A block with a mass m is pulled along a horizontal surface for a distance +x by a constant force F at an angle with respect to the horizontal. The coefficient of kinetic friction between block and table is µk. Is the force exerted by friction equal to µkmg?
(b) How much work is done by the friction force and by F? (Don't forget the signs.) (Use mu_k for µk, q for , and m, g, x, and F as appropriate.)

6. A hummingbird is able to hover because, as the wings move downwards, they exert a downward force on the air. Newton's third law tells us that the air exerts an equal and opposite force (upwards) on the wings. The average of this force must be equal to the weight of the bird when it hovers. If the wings move through a distance of 2.9 cm with each stroke, and the wings beat 67 times per second, determine the work performed by the wings on the air in 1 minute if the mass of the hummingbird is 3.0 grams.