A thrill-seeking student jumps off a bridge from the height H = 80.0 m above the water level. The student is attached to the bridge by an elastic cord so that she reaches zero velocity just as she touches the water. After some up-and-down bouncing, the student eventually comes to rest h = 20.0 m above the water level. What is the maximum speed reached by the student during the fall? Neglect air resistance and use 10.0 m/s2 for the acceleration due to gravity.
A particle starts at the origin and moves in the xy-plane with velocity vx
= w + ay, vy = u.
Let w = 2 m/s, u = 1 m/s, a = 1/s. Find the trajectory y(x) of
the particle. What is its distance from the origin when x = 6 m?
Consider a r = 0.5 cm radius copper sphere (ρ = 8.96 g/cm3)
moving through a fluid with viscosity η = 5 *10-3 Pa-s in
gravity-free space. At t = 0 it is at r = 0 and has a velocity of v
= 10 cm/s n. (n is a unit vector pointing in some
direction.) Stokes law gives the drag force acting on the sphere in terms
of the viscosity of the fluid.
F = -6πηrv.
Write down the equation of motion for the sphere and find r(t)
and the distance of the sphere from the origin when it comes to rest.
An object is sliding on a frictionless surface with velocity V0.
There is a track on the surface, which turns object backwards as shown by
the dashed
line in the figure. If the radius of the track is R and the coefficient of
kinetic friction
between object and track is μ, how long will it take for the object to make a 180
degree turn?
The size of the object is negligible compared to the radius of the track.
A satellite moves on a circular earth orbit that has a radius of 6700 km. The radius of Earth is 6371 km. A model airplane is flying on a 15 m guideline in a horizontal circle. The guideline is parallel to the ground. Find the speed of the plane such that the plane and the satellite have the same centripetal acceleration.