Questions from Calculus

Q: The figure shows the curve C traced by a particle with position

The figure shows the curve C traced by a particle with position vector r(t) at time t. (a) Draw a vector that represents the average velocity of the particle over the time interval 3 < t < 3.2. (b) Wr...

Q: An athlete throws a shot at an angle of 450 to the

An athlete throws a shot at an angle of 450 to the horizontal at an initial speed of 43 ft/s. It leaves his hand 7 ft above the ground. (a). Where is the shot 2 seconds later? (b). How high does the s...

Q: A projectile is launched with an initial speed of 40 m/

A projectile is launched with an initial speed of 40 m/s from the floor of a tunnel whose height is 30 m. What angle of elevation should be used to achieve the maximum possible horizontal range of the...

Q: Find a vector function that represents the curve of intersection of the

Find a vector function that represents the curve of intersection of the cylinder x2 + y2 = 16 and the plane x + z = 5.

Q: Find the velocity and position vectors of a particle that has the

Find the velocity and position vectors of a particle that has the given acceleration and the given initial velocity and position. a(t) = sin t i + 2 cos t j + 6t k, v (0) = 2k, r (0) = j - 4 k

Q: A ball rolls off a table with a speed of 2 ft

A ball rolls off a table with a speed of 2 ft/s. The table is 3.5 ft high. (a). Determine the point at which the ball hits the floor and find its speed at the instant of impact. (b). Find the angle...

Q: A cable has radius r and length L and is wound around

A cable has radius r and length L and is wound around a spool with radius R without over- lapping. What is the shortest length along the spool that is covered by the cable?

Q: Show that the curve with vector equation lies in a plane and

Show that the curve with vector equation lies in a plane and find an equation of the plane.

Q: If |r(t) | = 1 for all t

If |r(t) | = 1 for all t, then |r'(t) | is a constant.

Q: Different parametrizations of the same curve result in identical tangent vectors at

Different parametrizations of the same curve result in identical tangent vectors at a given point on the curve.