Alexis G.

asked • 02/10/22

Average velocity for a time period

The deck of a bridge is suspended 215 feet above a river. If a pebble falls off the side of the bridge, the height, in feet, of the pebble above the water surface after t seconds is given by y = 215 − 16t2.

(a)

Find the average velocity (in ft/s) of the pebble for the time period beginning when t = 3 and lasting the following amount of time.

1 Expert Answer

By:

Heriberto E. answered • 02/10/22

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Private Math and Physics Tutor with 8+ years of experience

Alexis G.

Given this, am I correct to say that if the time passed is .1 second, it would be 25.6 ft/s? Because then a is 3 and b is 3.1, so then t would be .1, correct? From there, you take 16t^2 = (16x(.1))^2 which is 2.56. Then since 215 is the distance from the bridge, that means in the .1 second it fell, it would have traveled the distance of 2.56ft correct? and then when you turn that into a full second rather than 1/10 of a second, it would be 25.6 ft/s correct? Or am I completely lost and confused?
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02/14/22

Heriberto E.

Times passed between what parameters? I mean, where are you considering the starting point and the ending point for this "time passed" that you are referring to? Is it from the start of the pebble's trajectory (i.e. when it fell off the side of the bridge) to when it hit the surface of the water? Or at the start of the average velocity in this problem to when it touched the surface of the water? I think you're implying the latter (the second one), but in order to avoid confusion (for yourself and others), it never hurts to specify! Trust me, it can only help you! The "b" you mention, which in the video I call t_b (t subscript b), is equal to √(215)/4 seconds or about 3.67 seconds. Remember, it's when y = 0 that the pebble hits the water which can be calculated via clever factoring or the quadratic formula. Please refer to the video for further detail. Therefore, the time difference for the average speed is from 3 seconds to 3.67 seconds. The time passed here would be Δt = 3.67 seconds - 3 seconds = 0.67 seconds. If you'd like more personalized clarification, you're more than welcome to set up a tutoring sessions with me here: https://www.wyzant.com/Tutors/HeriTutoringSpace
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02/15/22

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