Question

rate 1. True or False? Explain: a. If a car's speedometer is constant, then the car cannot be accelerating. b. Ifan =0 for a moving object, then the object cannot be accelerating. c. The arc length of a space curve depends on the parameterization. d. The curvature of a circle is the same as its radius. e. The normal component of acceleration is a function of both speed and curvature. 2. Projectile Motion: A projectile is launched with an initial velocity of 220 feet per second at a height of 4 feet and an angle of 45° with the horizontal a. Determine the vector valued function for the path of the projectile. b. Use your calculator to graph the path and approximate the maximum height and range of the projectile. Round feet to whole feet and seconds to two decimal places. Suggested window. Tmin=0, Tmax=4*, Tstep="/12 on (-10,1800, 0, 450] Xscl=200, Yscl=50. Use C. Calculate the maximum height and the range. Round feet to whole feet and seconds to two decimal places. d. Find (t). (I, and at e. Use your calculator to complete the table. Round speed to whole feet/sec. t (sec) 0.5 1.0 1.5 25 3.0 Speed (fls) 3. Air Traffic Control: Because of a storm, ground controllers instruct the pilot of a plane flying at an altitude of 4 miles to make a 90"turn and climb to an altitude of 4.2 miles. The model for the path of the plane during this maneuver is F(t) = (10 cos 10nt, 10 sin 10t, 4 + 4t), for Osts Where t is the time in hours and r is the distance in miles. a. Determine the speed of the plane b. Calculate ay and ay. Why is one of these equal to zero? 4. Speed: The smaller the curvature of a bend in the road, the faster a car can travel. it the maximum speed around a turn is inversely proportional to square root of the curvature. A formula for curvature is: ym k = 11+(2p/2, the curve in space C given by y=f(x) A car moving on the path y = x3, where x and y are measured in miles, can safely go 30 miles per hour at (1, 2). How fast can it go at 6-3)?

Answer 1

Ans-1: : ® since car's speedometer is constant that means rate of Change of speed is zeno is accelration is zewo (True le O since for any moving obect we have e two componant. Huizontal & Marmal it ano 9770 I uno so Boely avetrate linear: (false) yes, at nog n= n(t) yes, at y = yet) then are lengu: L=JJ1 + (dy jdet so depends on parameterization (True) ) since the curvature of the circle ..kah RK Rades al curvatur so o Recipocal al Radius heat equal. so (false).