A traveling wave on a string is described by y = 2 .0 sin [ 2 π ( t 0.40 + x 80 ) ] , where x and y are in centimeters and t is in seconds, (a) For t = 0, plot y as a function of x for 0 ≤ x ≤ 160 cm. (b) Repeat (a) for t = 0.05 s and t = 0.10 s. From your graphs, determine (c) the wave speed and (d) the direction in which the wave is traveling.
A traveling wave on a string is described by y = 2 .0 sin [ 2 π ( t 0.40 + x 80 ) ] , where x and y are in centimeters and t is in seconds, (a) For t = 0, plot y as a function of x for 0 ≤ x ≤ 160 cm. (b) Repeat (a) for t = 0.05 s and t = 0.10 s. From your graphs, determine (c) the wave speed and (d) the direction in which the wave is traveling.
where x and y are in centimeters and t is in seconds, (a) For t = 0, plot y as a function of x for 0 ≤ x ≤ 160 cm. (b) Repeat (a) for t = 0.05 s and t = 0.10 s. From your graphs, determine (c) the wave speed and (d) the direction in which the wave is traveling.
Part C
Find the height yi
from which the rock was launched.
Express your answer in meters to three significant figures.
Learning Goal:
To practice Problem-Solving Strategy 4.1 for projectile motion problems.
A rock thrown with speed 12.0 m/s and launch angle 30.0 ∘ (above the horizontal) travels a horizontal distance of d = 19.0 m before hitting the ground. From what height was the rock thrown? Use the value g = 9.800 m/s2 for the free-fall acceleration.
PROBLEM-SOLVING STRATEGY 4.1 Projectile motion problems
MODEL: Is it reasonable to ignore air resistance? If so, use the projectile motion model.
VISUALIZE: Establish a coordinate system with the x-axis horizontal and the y-axis vertical. Define symbols and identify what the problem is trying to find. For a launch at angle θ, the initial velocity components are vix=v0cosθ and viy=v0sinθ.
SOLVE: The acceleration is known: ax=0 and ay=−g. Thus, the problem becomes one of…
Physics for Scientists and Engineers: A Strategic Approach, Vol. 1 (Chs 1-21) (4th Edition)
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