1. A 50 kg roller coaster car is launched, from ground level, at 20 m/s. How fast will it be moving when it reaches the top of a loop, which is 12 m above the ground? 2. A 200 g model rocket is observed to rise 100 m above the ground after launch. What must have been the launch speed of the rocket at the ground?

3. (This one’s a toughie) A 10 kg monkey swings on a vine from a point which is 40 m above the jungle floor to a point which is 15 m above the floor. If the monkey was moving at 2 m/s initially, what will be his speed at the 15 m point?

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Astudent is given an assignment to demonstrate diffraction. he takes a photograph of a straw in a glass of water. the straw appears bent at the water level. which best describes this example? a) this is a good example of diffraction. b) this is an example of dispersion and not diffraction. c) this is an example of refraction and not diffraction. d) this is an example of reflection and not diffraction.

Use the frequency histogram to complete the following parts. ​(a) identify the class with the​ greatest, and the class with the​ least, relative frequency. ​(b) estimate the greatest and least relative frequencies. ​(c) describe any patterns with the data. female fibula lengths 30.5 31.5 32.5 33.5 34.5 35.5 36.5 37.5 38.5 39.5 0 0.05 0.1 0.15 0.2 0.25 length (in centimeters) relative frequency a histogram titled "female fibula lengths" has a horizontal axis labeled "length in centimeters" from 30.5 to 39.5 in increments of 1 and a vertical axis labeled "relative frequency" from 0 to 0.25 in increments of 0.05. the histogram contains vertical bars of width 1, where one vertical bar is centered over each of the horizontal axis tick marks. the approximate heights of the vertical bars are listed as follows, where the label is listed first and the approximate height is listed second: 30.5, 0.02; 31.5, 0.04; 32.5, 0.05; 33.5, 0.13; 34.5, 0.22; 35.5, 0.25; 36.5, 0.13; 37.5, 0.06; 38.5, 0.09; 39.5, 0.01. ​(a) the class with the greatest relative frequency is nothing to nothing centimeters. ​(type integers or decimals. do not round. use ascending​ order.)

(a) assume the equation x = at^3 + bt describes the motion of a particular object, with x having the dimension of length and t having the dimension of time. determine the dimensions of the constants a and b. (use the following as necessary: l and t, where l is the unit of length and t is the unit of time.) (b) determine the dimensions of the derivative dx/dt = 3at^2 + b. (use the following as necessary: l and t, where l is the unit of length and t is the unit of time.)