Aproton is initially moving west at a speed of 1.10 106 m/s in a uniform magnetic field of magnitude 0.281 t directed vertically upward. describe in detail the proton's trajectory, including its shape and orientation.

so here it will move in circle with radius 4.06 cm

Explanation:

As we know that proton is moving towards west while the magnetic field is vertically upwards

So here the force on the proton must be perpendicular to the velocity

So here we have

so here we have

since force is perpendicular to the velocity so here it must be centripetal force

here we have

so we have

so here it will move in circle with radius 4.06 cm

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initial speed when it is dropped is 150 ft/s

now at the same moment the acceleration due to gravity is perpendicular to its velocity

so as we know that

now we have centripetal acceleration a = 32 ft/s^2 as its perpendicular to velocity

while tangential acceleration at the same moment will be zero

so

now radius of curvature is given as

so the radius of curvature just after it is dropped is 703.125 ft