Related questions with answers

Chuck and Jackie stand on separate carts, both of which can slide without friction. The combined mass of Chuck and his cart, $m_{cart}$ , is identical to the combined mass of Jackie and her cart. Initially, Chuck and Jackie and their carts are at rest. Chuck then picks up a ball of mass $m_{ball}$ and throws it to Jackie, who catches it. Assume that the ball travels in a straight line parallel to the ground (ignore the effect of gravity). After Chuck throws the ball, his speed relative to the ground is $v_C$ . The speed of the thrown ball relative to the ground is $v_b$ . Jackie catches the ball when it reaches her, and she and her cart begin to move. Jackie's speed relative to the ground after she catches the ball is $v_J$ . When answering the questions in this problem, keep the following in mind: The original mass $m_{cart}$ of Chuck and his cart does not include the mass of the ball. The speed of an object is the magnitude of its velocity. An object's speed will always be a nonnegative quantity. What is Chuck's speed $v_C$ (relative to the ground) after he throws the ball?

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Question

If airplanes A and B are moving southwest with speed |VA|=550 mph, and north-west with speed |VB|=450 mph, respectively, what is the relative velocity V=VB-VA of B with respect to A?

Solution

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We put them in the $xy$ -plane, where positive $x$ -semiaxis represents east, while positive $y$ -semiaxis represents north. Thus, the velocities of airplanes are given by the following sketch (the angle between $\mathbf{v_B}$ and negative $x$ -semiaxis is $45^{\circ}$ since $B$ is moving northwest):