Question

3.48 q: the diagram below represents the path of a stunt car that is driven off a cliff, neglecting friction. compared to the horizontal component of the cars velocity at point a, the horizontal component of the cars velocity at b is (a) smaller (b) greater (c) the same 3.49 q: a 0.2 - kilogram red ball is thrown horizontally at a speed of 4 meters per second from a height of 3 meters. a 0.4 - kilogram green ball is thrown horizontally from the same height at a speed of 8 meters per second. compared to the time it takes the red ball to reach the ground, the time it takes the green ball to reach the ground is (a) one - half as great (b) twice as great (c) the same (d) four times as great

Explanation:

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Step1: Analyze horizontal motion

In the absence of air - friction, there is no horizontal force acting on the stunt car. According to Newton's first law, an object in motion will stay in motion with a constant velocity in the absence of a net force. The horizontal component of velocity \(v_x\) remains constant because \(F_x = 0\) and \(a_x=\frac{F_x}{m}=0\).

Step2: Compare horizontal velocities

Since there is no acceleration in the horizontal direction, the horizontal component of the car's velocity at point A is the same as the horizontal component of the car's velocity at point B.

Step1: Consider vertical motion

The vertical motion of a horizontally - thrown object is a free - fall motion. The vertical displacement \(y\) of an object in free - fall is given by the equation \(y = v_{0y}t+\frac{1}{2}gt^{2}\), where \(v_{0y} = 0\) (thrown horizontally), so \(y=\frac{1}{2}gt^{2}\), and \(t=\sqrt{\frac{2y}{g}}\).

Step2: Analyze time of fall

The time of fall \(t\) depends only on the height \(y\) and the acceleration due to gravity \(g\). Since both the red and green balls are thrown from the same height \(y = 3m\) and \(g\) is constant (\(g\approx9.8m/s^{2}\)), the time it takes for each ball to reach the ground is the same, regardless of their horizontal speeds and masses.

Answer:

C. the same

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