ExamStudyAid
You are not logged in.
A car moves east at 20 m/s relative to the road. A bird flies west at 5 m/s relative to the road. Describe the reference frame of a passenger in the car and state what velocity the passenger measures for the bird.
Sign in and upgrade to Premium to write and mark your own answer.
The passenger's reference frame moves east at 20 m/s relative to the road. In that frame, the bird approaches at 20 + 5 = 25 m/s westward, because the car's motion and the bird's motion are in opposite directions.
Two observers watch the same ball. Observer A stands on the ground. Observer B rides a skateboard at constant velocity. Indicate whether the two observers measure the same acceleration for the ball? Justify your answer.
Sign in and upgrade to Premium to write and mark your own answer.
Both observers measure the same acceleration. The acceleration of any object is identical in all inertial reference frames because each frame differs only by a constant velocity, and the derivative of a constant is zero.
A train moves east at 25 m/s relative to the ground. A passenger walks toward the rear of the train at 1.5 m/s relative to the train. Determine the passenger's velocity relative to the ground.
Sign in and upgrade to Premium to write and mark your own answer.
Positive direction: east. Equation used: $${v}_{PG}={v}_{PT}+{v}_{TG}$$ Given: $${v}_{PT}=-1.5\text{ m/s (walking west relative to train)}$$ $${v}_{TG}=+25\text{ m/s}$$ Working: $${v}_{PG}=-1.5+25=23.5\text{ m/s}$$ The passenger moves east at 23.5 m/s relative to the ground.
An airplane flies at 60 m/s due north relative to the air. A crosswind blows at 25 m/s due west relative to the ground. Calculate the airplane's speed relative to the ground.
Sign in and upgrade to Premium to write and mark your own answer.
Equation used: $${v}_{AG}=\sqrt{{v}_{AG,x}^{2}+{v}_{AG,y}^{2}}$$ Given: $${v}_{AG,x}=-25\text{ m/s (west)}$$ $${v}_{AG,y}=60\text{ m/s (north)}$$ Working: $${v}_{AG}=\sqrt{(-25{)}^{2}+(60{)}^{2}}=\sqrt{625+3600}=\sqrt{4225}=65.0\text{ m/s}$$ The airplane’s speed relative to the ground is 65.0 m/s.
Two cars travel on a straight highway. Car A moves at 30 m/s east and Car B moves at 20 m/s east, both relative to the ground. The driver of Car A brakes, decelerating at 2.0 m/s² westward. Indicate whether an observer in Car B measures the same, greater, or lesser magnitude of acceleration for Car A compared to a ground observer? Justify your response.
Sign in and upgrade to Premium to write and mark your own answer.
The observer in Car B measures the same magnitude of acceleration (2.0 m/s²). Car B moves at constant velocity, so it defines an inertial frame. The acceleration of any object is identical in all inertial reference frames. Only velocities shift between frames; acceleration does not.
A student claims that because two observers measure different velocities for the same ball, they must also measure different net forces on the ball. Indicate whether this claim is consistent with Newton's second law? Justify your reasoning.
Sign in and upgrade to Premium to write and mark your own answer.
The claim is not consistent with Newton’s second law. Different inertial observers measure different velocities, but all measure the same acceleration. Because ${\vec{F}}_{\text{net}}=m\vec{a}$ and both $m$ and $\vec{a}$ are identical across inertial frames, the net force is also identical. Different velocities do not imply different forces.