Problem 3.69 Observer 1 rides in a car and drops a ball from rest straight downw

Question

Problem 3.69 Observer 1 rides in a car and drops a ball from rest straight downward, relative to the interior of the car. The car moves horizontally with a constant speed of 3.45 m/s relative to observer 2 standing on the sidewalk. Part A What is the speed of the ball 1.00 s after it is released, as measured by observer 2? Express your answer to three significant figures and include appropriate units. Value Units Submit My Answers Give Up Part B What is the direction of travel of the ball 1.00 s after it is released, as measured relative to the horizontal by observer 2? Express your answer to three significant figures and include appropriate units. below horizontal Value Units

Explanation / Answer

part A:

as per observer 2, the ball has two components of velocity at any given time t.

the horizontal velocity is due to the car's velocity and it is constant at 3.45 m/s

initial vertical speed is 0 m/s and it grows due to acceleration due to gravity of 9.8 m/s^2

so after 1 seconds, vertical speed=initial speed+acceleration*time

=0+9.8*1=9.8 m/s

so total speed=sqrt(horizontal speed^2+vertical speed^2)

=sqrt(3.45^2+9.8^2)=10.38953 m/s

in 3 significant figures, answer is 10.4 m/s
part B:

angle with horizontal =arctan(vertical speed/horizontal speed)

=arctan(9.8/3.45)=70.6 degrees

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