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If a particle moves through space along a curve C having curvature k=0 at a point P, then the tangential component of the acceleration of?
the particle at P is 0. True or False?
1 AnswerPhysics5 years agoTrue or false: If the unit tangent vector T and the unit normal vector N exist at a point P on a parametrized curve C in 3D, then the?
binormal vector B of C at P is a normal vector to the osculating plane of C at P.
1 AnswerMathematics5 years agoTrue or false: The force acting on a particle moving along the curve r(t) = (sin(2t), -cos(2t), 0) is directed toward the origin at every?
point on the curve. Please explain!
1 AnswerMathematics5 years agoA cannon is placed on high ground 24ft above a target that is 1000ft away horizontally. It fires a projectile upward at a 45 degree angle?
with an initial velocity of v sub 0 ft/s. What value of v sub 0 ft/s is necessary for the projectile to hit the target? The acceleration due to gravity is g=32 ft/s^2. Please explain!
1 AnswerPhysics5 years agoThe following is a quotation form an article in The American Mathematical Monthly, titled "Curvature in the Eighties" by Rober Osserman?
"Curvature also plays a key role in physics. The magnitude of a force required to move an object at constant speed along a curved path is, according to Newton's laws, a constant multiple of the curvature of the trajectories". Use magnitude of F = (m)(magnitude of acceleration) and the decomposition of acceleration into tangential and normal components to make an equation that correctly expresses the above statement as a mathematical equation.
1 AnswerPhysics5 years agoGiven a particle that moves according to r(t)=(t^2, (t+(t^3)/3), (t-(t^3)/3)), write the acceleration a of the particle in the form?
including the normal and tangential components of the acceleration when t=0. Please explain!
2 AnswersPhysics5 years agoA catapult located at ground level launches a banana cream pie toward a clown standing on a platform 280 ft away. The initial speed of the?
pie is 70(sqrt 2) and the angle of elevation is 45 degrees. The acceleration due to gravity is g=32ft/s^2. How high above the ground level should the platform be raised so that the pie hits the clown? Please explain!
2 AnswersPhysics5 years agoA segment of roller coaster track is in the shape of a parametric curve given by r(t)=(2t, t^2, (t^3)/3) with t between -5 and 5. Find a?
formula for the curvature of the track at r(t). Please explain!
3 AnswersMathematics5 years agoA curve has a vector equation r(t)= (ln(sin t), ln(cos t), (sqrt 2)t), where t is between 0 and pi/2. Find an equation of the osculating?
plane to the curve at the point ((-ln 2)/2, (-ln 2)/2, pi/(2 sqrt 2)). Please explain!
1 AnswerMathematics5 years agoAdam and Barbara each toss a frisbee. Adam's frisbee has initial position r(0)=(0,0,-1) and velocity v1(t)=(1,8t,3t^2), and Barabara's?
frisbee has initial position q(0)=(0,3,-4) and velocity v2(t)=(2t,1,4). At what times do the frisbess collide?
4 AnswersMathematics5 years agoFind the parametric equations for the tangent line to the curve with vector equation given below at the point (0,-1, pi^2).?
r(t)=(cot t, cos 2t, 4t^2). Please explain!
1 AnswerMathematics5 years agoLet r(t)= (f(t), g(t), h(t)). If the unit tangent vector at the point where t=11 is T(11)= ((sqrt 11)/4, (1/2), (1/4)) and g(t)=4e^(t-11),?
what is h(t)? Please explain!
1 AnswerMathematics5 years ago
