Let r(t) = (4sin 21)i + (4cos 2r)j– (e“ )k, be the position of particle in space at time . Find the velocity, speed and acceleration of the particle at -0. Problem 2: (2 marks) A projectile is fired from the origin over the horizontal ground at an initial speed of 900 m/sec and a launch angle of 600 (i) When and how far away will the projectile strike? (i) How high overhead will the projectile be when it is 9 km downrange. Problem 3: (2 marks) Find the curvature for the curve r(t) = (6sin 2t)i + (6cos 2t)j+ 5tk

Q: 14. The position vector of a particle of mass 2kg is given as a function of time by: I r= = (4i + 2t…

A: Solution:-

Q: 8.) FIND ALL DERIVATIVES OF y^(n) OF THE FUNCTION y = square root of (x+5).

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A: Given: In this problem, the given details are, A particle moving in x-y plane at velocity,…

Q: - The position of an object moving on a line is given by s(t) = 6t2 – t°, t > 0,

A: Solve

Q: (a) Find the veloc v(t) = (sin(t) +t co- (b) Find the accel a(t) = (2 cos(1) –1s cos(t) -ts (c) Find…

A: Given that : The position function is r(t) = t sin (t) i + t cos (t) j + 4t2 k.

Q: Let 7 (t) = (2 – 5t2)i – (9t°)j – 4tk be the position of particle in space at time t. The %3D speed…

A: The speed of the particle at t=0 is 4

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Q: An object moves in space with acceleration a(t) = 12t²i+6tj+2k. When t = 0, the object is at (1, 0,…

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Q: 2. A particle is moving according to the position function s(t) = - 2t3 – 6t² + 9t, where s is in mm…

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Q: 4. Consider the motion of a particle as described by 1 1 r(t) = = t, Write the acceleration vector…

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Q: A particle moves along the graph of y = cos r so that the r-component of acceleration is always 2.…

A: Use the given information carefully.