Question

A cart is propelled over an xy plane with acceleration components ax- 4.4 m/s2 and ay--1.7 m/s2. Its initial velocity has components vox-6.2 m/s and voy 11.0 m/s. In unit-vector notation, what is the velocity of the cart when it reaches its greatest y coordinate?

Answer 1

since, acceleration in y direction is negative
so, at some point velocity in y direction must be zero
and that point is greatest y coordinate
so, velocity in y direction at greatest y coordinate will be zero

so,
velocity at greatest y coordinate = velocity in x direction

let greatest y coordinate be y
then use,
Vfy - Viy = ay*t
0 - 11.0 = -1.7*t
t = 11.0/1.7
= 6.47 s

so, velocity in x direction
Vfx = Vix + ax*t
= 6.2 + 4.4*6.47
= 6.2 + 28.468
= 34.668 m/s
= 34.7 m/s

so,
velocity at greatest y coordinate = velocity in x direction
= 34.7 m/s

Answer: 34.7 m/s