Ch 03: 2D Motion (Projectile Motion)WorksheetSee all chapters
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Ch 01: Units & Vectors
Ch 02: 1D Motion (Kinematics)
Ch 03: 2D Motion (Projectile Motion)
Ch 04: Intro to Forces (Dynamics)
Ch 05: Friction, Inclines, Systems
Ch 06: Centripetal Forces & Gravitation
Ch 07: Work & Energy
Ch 08: Conservation of Energy
Ch 09: Momentum & Impulse
Ch 10: Rotational Kinematics
Ch 11: Rotational Inertia & Energy
Ch 12: Torque & Rotational Dynamics
Ch 13: Rotational Equilibrium
Ch 14: Angular Momentum
Ch 15: Periodic Motion (NEW)
Ch 15: Periodic Motion (Oscillations)
Ch 16: Waves & Sound
Ch 17: Fluid Mechanics
Ch 18: Heat and Temperature
Ch 19: Kinetic Theory of Ideal Gasses
Ch 20: The First Law of Thermodynamics
Ch 21: The Second Law of Thermodynamics
Ch 22: Electric Force & Field; Gauss' Law
Ch 23: Electric Potential
Ch 24: Capacitors & Dielectrics
Ch 25: Resistors & DC Circuits
Ch 26: Magnetic Fields and Forces
Ch 27: Sources of Magnetic Field
Ch 28: Induction and Inductance
Ch 29: Alternating Current
Ch 30: Electromagnetic Waves
Ch 31: Geometric Optics
Ch 32: Wave Optics
Ch 34: Special Relativity
Ch 35: Particle-Wave Duality
Ch 36: Atomic Structure
Ch 37: Nuclear Physics
Ch 38: Quantum Mechanics

Solution: A swimmer is capable of swimming 0.80 m/s in still water.(a) At what upstream angle must the swimmer aim, if she is to arrive at a point directly across a 55 m wide river whose current is 0.50 m/s ?(b) How long will it take her?

Solution: A swimmer is capable of swimming 0.80 m/s in still water.(a) At what upstream angle must the swimmer aim, if she is to arrive at a point directly across a 55 m wide river whose current is 0.50 m/s ?(b

Problem

A swimmer is capable of swimming 0.80 m/s in still water.

(a) At what upstream angle must the swimmer aim, if she is to arrive at a point directly across a 55 m wide river whose current is 0.50 m/s ?

(b) How long will it take her?

Solution

Whenever we have a problem about a boat or swimmer crossing a river, it's safe to assume it's a two-dimensional relative motion problem. The steps to solve a problem like this are going to be:

  1. Organize information: the variables involved in a problem like this are velocities, distances, and time. It's always a good idea to draw yourself a diagram and label knowns to help you visualize the information!
  2. Combine velocities.
  3. Solve for the target variable.

In general, the equation we'll use to add velocities is:

vPA=vPB+vBA

In this problem, the swimmer has some velocity compared to the water of the river, and the river also moves with a velocity relative to the ground. If someone on the riverbank measured the swimmer's velocity, it would be the sum of those two vectors—we'll call that the "effective velocity" or veff.

veff=vs+vr

We may also need the equation relating constant velocity to displacement:

v=rt

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