A proton moves at 4.60 times 10^5 m/s in the horizontal direction. It enters a u

Question

A proton moves at 4.60 times 10^5 m/s in the horizontal direction. It enters a uniform vertical electric field with a magnitude of 7.80 times 10^3 N/C. Ignore any gravitational effects. Find the time interval required for the proton to travel 6.00 cm horizontally Find its vertical displacement during the time interval in which it travels 6.00 cm horizontally. (Indicate direction with the sign of your answer.) Find the horizontal and vertical components of its velocity after it has traveled 6.00 cm horizontally

Explanation / Answer

A. The E-field has no effect on the proton's horizontal motion. So the time it takes to go 0.06 meters is:
time = distance/velocity
time = 0.06/(4.6*10^5)
time = 1.3043*10^-7 sec

B. The proton accelerates vertically because of the E-field:
F=qE
ma=qE
a=(q/m)E
a=9.58 *107 * 7.8*10^3
a=7.47 *10^11 m/s2
We have the vertical acceleration and we found the time in part A, now we need the displacement:
y=(1/2)at^2 no initial y-velocity
y=(1/2)(7.47 *10^11)(1.3043*10^-7)^2
y=6.353*10^-3 m

C. The vertical velocity we can easily get:
v=at since intial vertical velocity was zero
v=(7.47 *10^11)(1.3043*10^-7)
v=97431.21 m/s
The horizontal velocity was never changed
v=4.6*10^5 m/s
So we have (vx,vy)=(4.6*10^5, 9.7*10^4) m/s

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