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Ph with Moeron or a Particle, As shown, a (char initial speed ve 10 m/s at an angle e-60 a region of uniform electric field F Eaj in 10 N/C. CS (a) What are the erations in the x and directions, a. and a Are these Constant or of time? y (b) What are v and (thexand y components of the these constant or functions of time? velocity)7Are (c) hat are x(t) and y thexand y positions ofthe particle as functions of time? (d) What is the maximum height the particle reaches? How long after launch does this happen?

Solution

total force on particle = (QE) j + mg(-j)

Q is negative.

so F = (QE + mg ) (-j)

F = ma

a = 0i - (QE + mg)/m (j)

acceleration in x direction = 0

in y direction = - (QE + mg) / m

b) initallly ux = v0 cos60

uy = v0 sin60

vx(t) = ux + ax*t = v0cos60 + 0.t

vx(t) = v0 cos60

vy(t) = uy + ay*t = v0 sin60 + (-(QE + mg)/m )t

vy (t) = v0sin60 - (QE/m)t - gt

c) at maximum vertical velocity becomes zero.

vy (t) = v0sin60 - (QE/m)t - gt = 0

t = v0sin60 / (QE + mg)/m = mv0sin60 / (QE + mg)

for h, using vf^2 - vi^2 = 2ah

0 - (vo sin60)^2 = 2 ( -(QE + mg)/m )h

h = m(v0 sin60)^2 /2(QE + mg)