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Problem 70 Hard Difficulty

Protons are projected with an initial speed $\tau_{b}=9550 \mathrm{m} / \mathrm{s}$ into a region where a uniform electric field of magnitude $E=$ 720 $\mathrm{N} / \mathrm{C}$ is present (Fig. $\mathrm{P} 15.70 ) .$ The protons are to hit a target that lies a horizontal distance of 1.27 $\mathrm{mm}$ from the point where the protons are launched. Find (a) the two projection
angles $\theta$ that will result in a hit and (b) the total duration of flight for each of the two trajectories.

Answer

a. $53.08^{\circ}$
b. $2.21 \times 10^{-7} \mathrm{s}$

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Video Transcript

harassed rains like start or discussion. Suppose a proton's are protected with the initials speed off 955 zero Meet upper second to hit the target. Suppose add distance. Are is the target okay? And the poor, The projecting angle is theta No, the a broad. The target that is hitting by the proton is at a distance off 1.27 millimeter. That is changes given in our example 1.27 millimeter that is going toe toe seven into 10. Respond ministry meter. Okay. And the electric field is in vision Isn't downward direction and it real bills 7 20 Newton Bakula 7 20 Newton back. Will Imo love we have toe find Aga Tita. Okay, so basically engine will we have the formal off range in the projectile motion is you square sign do Tita by G But this isn't a general case where mg a downer force is applying on the particle in our body. But in this case, in the case off the floor tone Onley electrostatic forces applying on the downward direction that is gooey. So instead, off G in this case will use que Eva Ah, in general case where we take mg Donald Force that is equivalent to electrostatic force. So basically from Jill comes or to Rick, you buy em. So instead off G, we will use Cube if I am in this case because there's no m g force in downward direction acting instead off this days electrostatic force that is QE do toe. This electric force is acting on our particles that is brought on. So after solving this, scientists signed Putin will be are into a few We buy em born you squid and he will be one bite to sign in words are you e by Ammu Square. Now we have to put the values so Tita will be won by toe signing. Worse value off ranges given 1.27 to 10 years for ministry meter. The charge on the Pro Tony's 1.69 in took 10 dress par minus 19 and the electric Friel is 7 20 The Marcelin brought own is 1.6 into templates for minus a ties. Cagey and initially lost is 9550 Meet up a second square, so by solving days we will get the value off titter approximately equal to 53 degrees. Okay. We also have to find the time period off taken by Proton to hit the target. So he will be to you. Sign Tita by G instead off G. We will use to your sign data. You see by em. So now, putting all the values that is too into 955 Jiro into sign 53 degree, 1.6 into templates for minus 19 into 77 p 7 20 actually of electric field by 1.6 in pretend this par minus 27 K g. We will get a time better off 2.21 in tow. 10 days by minus eight second. Okay. Well, this is all for me for this video. I hope you will like the video. Thank you.

Other Schools
Top Physics 102 Electricity and Magnetism Educators
Elyse G.

Cornell University

Andy C.

University of Michigan - Ann Arbor

Farnaz M.

Other Schools

Aspen F.

University of Sheffield

Physics 102 Electricity and Magnetism Bootcamp

Lectures

Join Bootcamp