# Physics problems to solve

*label*Physics

*timer*Asked: Sep 20th, 2015

**Question description**

The coordinates of an object moving in the xy plane vary with time according to the equations x = −5.00 sin(ωt)
and y = 4.00 − 5.00 cos(ωt), where ω is a constant, x and y are in meters, and t is in seconds. (a) Determine
the components of velocity of the object at t = 0. (b) Determine the components of acceleration of the object
at t = 0. (c) Write expressions for the position vector, the velocity vector, and the acceleration vector of the
object at any time t > 0. (d) Describe the path of the object in an xy plot.

A golf ball is hit off a tree at the edge of a cliff. Its x and y coordinates as functions of time are given by
x = 18.0t and y = 4.00t − 4.9t
2
, where x and y are in meters and t is in seconds. (a) Write a vector expression
for the ball’s position as a function of time, using the unit vectors ˆi and ˆj. By taking derivatives, obtain
expression for (b) the velocity vector ~v as a function of time and (c) the acceleration vector ~a as a function of
time. (d) Next use unit-vector notation to write expressions for the position, the velocity, and the acceleration
of the golf ball at t = 3.00 s.