Problem 1: A car moves along a horizontal road with constant velocity v 0 = v 0x
ID: 1275329 • Letter: P
Question
Problem 1: A car moves along a horizontal road with constant velocity v0 =v0xi until it encounters a smooth inclined hill, which it climbs with constant velocityv1 = v1xi + v1yj as indicated in the figure. The car uniformly and instantaneously changes its velocity at the road-hill intersection. Let the origin of the Cartesian coordinate system be at the car?s initial position.
If the car moves for equal times along the road and hill, create an expression for its average velocity vector vave in terms ofv0x, v1x, and v1y during the total time interval and the unit vectors i and j.
Create an expression for the direction of the car
Explanation / Answer
ow can anything happen "during the transition" if the transition is instantaneous? The expression for the magnitude of the acceleration would end up with a zero in the denominator, so would be undefined.
Oh well, the DIRECTION of the acceleration would have the property
tan (theta) = v1y / (v1x - v0x),
and if it happens that v1x=v0x, then theta = 90 degrees.
If it happens that the SPEED of the car stays the same,
then v1x will be a bit less than v0x,
and theta will be a bit more than 90 degrees
vave = 0.5(v0x+v1x)i+v1yj/2