Aperson with a remote montain cabin plansto
install her own hydroelectric plant. a nearby stream is 3.00mwide
and 0.500m deep. water floes at 1.20m/s over the brink of
awaterfall 5.00m high. the manufacturer promises only
25.0%efficiency in converting the pe of the water-earth system
intoelectric energy. find the power she can generate.

In an old-fashioned amusement park ride, passengers stand inside a 3.0-m-tall, 5.0-m-diameter hollow steel cylinder with their backs against the wall. the cylinder begins to rotate about a vertical axis. then the floor on which the passengers are standing suddenly drops away! if all goes well, the passengers will “stick” to the wall and not slide. clothing has a static coefficient of friction against steel in the range 0.60 to 1.0 and a kinetic coefficient in the range 0.40 to 0.70. part a what is the minimum rotational frequency, in rpm, for which the ride is safe? express your answer using two significant figures. f f = rpm

Asailboat is traveling to the right when a gust of wind causes the boat to accelerate leftward at 2.5m/s2 for 4s. after the wind stops, the sailboat is traveling to the left with a velocity of 3.0m/s.assuming the acceleration from the wind is constant, what was the initial velocity of the sailboat before the gust of wind? answer using a coordinate system where rightward is positive.

Avector a⃗ has a length of 8.6 m and points in the negative x direction. find the x component of the vector −3.7a⃗ .