Cyclist's speed at crest of hill & frictional force on motion of a car

A 82.3-kg skier rides a 2860-m-long lift to the top of a mountain. The lift makes an angle of 16.6° with the horizontal. What is the change in the skier's gravitational potential energy?

A cyclist approaches the bottom of a gradual hill at a speed of 28.7 m/s. The hill is 8.84 m high, and the cyclist estimates that she is going fast enough to coast up and over it without pedaling. Ignoring air resistance and friction, find the speed at which the cyclist crests the hill.

A 1100-kg car is being driven up a 9.21° hill. The frictional force is directed opposite to the motion of the car and has a magnitude of 510 N. A force F is applied to the car by the road and propels the car forward. In addition to these two forces, two other forces act on the car: its weight W and the normal force FN directed perpendicular to the road surface. The length of the road up the hill is 230 m. What should be the magnitude of F, so that the net work done by all the forces acting on the car is 198 kJ?

A 2.00 x 10^3 kg car rounds a circular turn of a radius 20.0 m. If the road is flat and the coefficient of static friction between the tires and the road is 0.70, how fast can the car go without skidding?

Car taking an un-banked circular turn:
A car is safely negotiating an un-banked circular turn at a speed of 21m/s. The max static frictionalforce acts on the tires. Suddenly a wet patch in the road reduces the maximum static frictionalforce by a factor of three. If the car is to continue safely around the curve, to what spe

A 63 kg skier coasts up a snow-covered hill that makes an angle of 25 degrees with the horizontal. The initial speed of the skier is 6.6 m/s. After coasting a distance of 1.9 m up the slope, the speed of the skier is 4.4 m/s.
(a) Find the work done by the kinetic frictionalforce that acts on the skis.
(b) What is the magni

Tom drives a car to climb a 100 m up hill road with a slope of 30 degrees(from horizontal). The total mass of Tom and the car is 2000 kg. Tom wants to drive through this up-hill road in 10 s. You can assume g = 9.8 m/s^2, the friction, air drag, rolling resistance can be ignored. Please determine the engine power needed for T

A 1380 kg car is moving due east with an initial speed of 27.0 m/s. After 8.00 s the car has slowed down to 17.0 m/s. What is the magnitude and direction of the net force that produces the deceleration.

"If a bicyclist of mass 69.0 (including the bicycle) can coast down a 6.90 degree hill at a steady speed of 5.60 km/hr because of air resistance, how much force must be applied to climb the hill at the same speed?"

Please see attachment. Thank You your help is greatly needed.
1. A ball moves with a constant speed of 4 m/s around a circle of radius 0.25 m. What is the period of the motion?
2. A racecar is traveling at constant speed around a circular track. What happens to the centripetal acceleration of the car if the speed is doubled

A car moving at 25 m/s drives over the top of a hill. The top of the hill forms an arc of a vertical circle 121 meters in diameter.
i) What is the centripetal force holding the car in the circle?
ii) What, therefore, is the normal force between the car's tires and the road?

24. A 0.30 kg puck, initially at rest on a frictionless horizontal surface, is struck (inelastically) by a 0.20 kg puck that is initially moving along the x-axis with a velocity of 2.0 m/s. After the collision, the 0.20 kg puck has a speed of 1.0 m/s at an angle of 53° to the +x-axis. Determine the magnitude and direction of th