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(II) A person in the passenger basket of a hot-air balloon throws a ball horizontally outward from the basket with spced 10.0 $\mathrm{m} / \mathrm{s}$ (Fig. 52$)$ . What initial velocity (magnitudeand direction) does the ball have relative to a person standing on the ground (a) if the hot-air balloon is rising at 5.0 $\mathrm{m} / \mathrm{s}$ relative to the ground during this throw,(b) if the hot-air balloon is descending at 5.0 $\mathrm{m} / \mathrm{s}$ relative to the ground.

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a) $27^{\circ}$ above the horizontalb) $27^{\circ}$ below the horizontal

Physics 101 Mechanics

Chapter 3

Kinematics in Two or Three Dimensions; Vectors

Motion Along a Straight Line

Motion in 2d or 3d

Newton's Laws of Motion

Rotation of Rigid Bodies

Dynamics of Rotational Motion

Equilibrium and Elasticity

University of Michigan - Ann Arbor

Simon Fraser University

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In physics, a rigid body is an object that is not deformed by the stress of external forces. The term "rigid body" is used in the context of classical mechanics, where it refers to a body that has no degrees of freedom and is completely described by its position and the forces applied to it. A rigid body is a special case of a solid body, and is one type of spatial body. The term "rigid body" is also used in the context of continuum mechanics, where it refers to a solid body that is deformed by external forces, but does not change in volume. In continuum mechanics, a rigid body is a continuous body that has no internal degrees of freedom. The term "rigid body" is also used in the context of quantum mechanics, where it refers to a body that cannot be squeezed into a smaller volume without changing its shape.

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In physics, rotational dynamics is the study of the kinematics and kinetics of rotational motion, the motion of rigid bodies, and the about axes of the body. It can be divided into the study of torque and the study of angular velocity.

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so he were going to say upwards is positive for vertical motion. So we can say that, um, the the X is gonna equal 10 0.0 meters per second. Of course, V, why would equal positive 5.0 meters per second and we considered the velocity vector in vector notation would be 10.0 meters per second I hat plus 5.0 meters per second j hat. To find the magnitude, this would be equal to the square root of the sum of the squares. So 10.0 squared plus 5.0 squared all to the 1/2 power. Simply take a square root. This is equaling 11 0.2 meters per second. Ah, so this would be the magnitude And then to find a direction, we would take our tent of the wind component five divided by the x component. 10 so tangent of 1/2 and this is equaling 27 degrees. We have a positive why and a positive X. So essentially, we're in the first quadrant, so it would be 27 degrees above positive X axis, so I'd be for party for part B. Ah, here. The only change would be going downwards. So now the why initial or other reasons it's a d y. I would be equal to negative 5.0 meters per second. So here the velocity vector would be 10 0.0 meters per second. I hat minus 5.0 meters per second. J hat. However, here the magnitude because the absolute value of the of both of the components are exactly the same. The magnitude is also going to be the exact saying. So the magnitude here it would be again 11.2 meters per seconds. Direction would be equal to again 27 degrees. However, we have a positive X and a negative. Why? So here were essentially in the fourth quadrant, so this would be 27 degrees below the positive X axis. So this would be your answer for part B. That is the end of the solution. Thank you for watching

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