Question

a car traveling at the legal speed limit has velocity +v_car with respect to the road. you are in another car traveling in the opposite direction at the legal speed limit with respect to the road. as the first car approaches you, what is its velocity relative to you? -2v_car +v_car v_car +2v_car question 6 the following questions refer to the following situation. in a circus parade, a clown standing on a float moving at a constant forward speed drops a fake dumbbell. a child in the bleachers on the sidewalk observes the dumbbell. ignore air resistance. the clown and the child would agree about which of the following observations? all of the above the vertical distance the dumbbell falls the initial vertical velocity of the dumbbell the time interval for the dumbbell to fall

Explanation:

Step1: Define velocities

Let the velocity of the first - car with respect to the road be $\vec{v}_{1r}= + v_{car}$ and your velocity with respect to the road be $\vec{v}_{yr}=-v_{car}$.

Step2: Use relative - velocity formula

The relative - velocity formula is $\vec{v}_{1y}=\vec{v}_{1r}-\vec{v}_{yr}$. Substitute the values: $\vec{v}_{1y}=v_{car}-(-v_{car}) = 2v_{car}$.

for second question:
The vertical motion of the dumbbell is a free - fall motion. The initial vertical velocity of the dumbbell $v_{0y} = 0$ (it is just dropped), the vertical distance it falls is given by $y = v_{0y}t+\frac{1}{2}gt^{2}=\frac{1}{2}gt^{2}$ (since $v_{0y} = 0$), and the time interval for it to fall is $t=\sqrt{\frac{2y}{g}}$. These vertical - motion parameters are the same for both the clown (in the non - inertial frame of the float) and the child (in the inertial frame of the sidewalk) because the horizontal motion of the float does not affect the vertical free - fall motion. So, they would agree on the vertical distance the dumbbell falls, the initial vertical velocity of the dumbbell, and the time interval for the dumbbell to fall.

Answer:

$+ 2v_{car}$