Let r(t) = < 1t+t,t-t,2t>. At which point(s) is the normal plane of this curve parallel...

 

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Let r(t) = < 1t+t,t-t,2t>. At which point(s) is the normal plane of this curve parallel to the plane 12x - 4y + 2z=0? QUESTION 7 A projectile is released from (3,0) with an initial speed of 40 m/s at an elevation angle of 30 degrees. Assume, for ease of calculation, that the acceleration due to gravity is 10 m/s downwards (i.c., in the negative y direction.) (a). Find the position and velocity functions of the projectile. (b). Find the maximum height the projectile reaches. (c). At what times is the projectile at a height which is three quarters of its maxi- mum height? QUESTION 8 An object moves in space with position function r(t) = <1 r(t) = Find its velocity, acceleration, and speed functions. QUESTION 9 An object of mass 2 moves with position function r(t) = < 5 cos(t) +1,3 sin(t)-1,-4 sin(t) + 2 >. (a). Find the speed of this object at time t. (b). Find the force vector acting on this object at time t = /3. Show that it points from the object towards the point (1,-1,2). That is, show that it is in the same direction as the vector from the object to (1,-1,2). (c). Find the object's tangential and normal components of acceleration at time t. QUESTION 10 A particle moves with position function r(t) = < -21, t, 312 >. Find its tangen- tial and normal components of acceleration at t= 0 and at t = 1. Let r(t) = < 1t+t,t-t,2t>. At which point(s) is the normal plane of this curve parallel to the plane 12x - 4y + 2z=0? QUESTION 7 A projectile is released from (3,0) with an initial speed of 40 m/s at an elevation angle of 30 degrees. Assume, for ease of calculation, that the acceleration due to gravity is 10 m/s downwards (i.c., in the negative y direction.) (a). Find the position and velocity functions of the projectile. (b). Find the maximum height the projectile reaches. (c). At what times is the projectile at a height which is three quarters of its maxi- mum height? QUESTION 8 An object moves in space with position function r(t) = <1 r(t) = Find its velocity, acceleration, and speed functions. QUESTION 9 An object of mass 2 moves with position function r(t) = < 5 cos(t) +1,3 sin(t)-1,-4 sin(t) + 2 >. (a). Find the speed of this object at time t. (b). Find the force vector acting on this object at time t = /3. Show that it points from the object towards the point (1,-1,2). That is, show that it is in the same direction as the vector from the object to (1,-1,2). (c). Find the object's tangential and normal components of acceleration at time t. QUESTION 10 A particle moves with position function r(t) = < -21, t, 312 >. Find its tangen- tial and normal components of acceleration at t= 0 and at t = 1.