A vector in the xy plane has a magnitude of 25 m and x component of 12 m. What i

Question

A vector in the xy plane has a magnitude of 25 m and x component of 12 m. What is its angle with the positive x axis? In getting ready to slum-dunk the ball, a basketball player starts from rest and sprints to a speed of 6.0 m/s in 1.5s. Assuming that the player accelerates uniformly, determine the distance he runs. An airplane is moving horizontally with a constant velocity of (+ 115 m/s) at altitude of 1050 m. The directions to the right and upward have been chosen as the positive directions. The plane releases a "care package' that falls to the ground along a curved trajectory. Ignoring air resistance, determine the time required for the package to hit the ground. A force vector has a magnitude of 720 N and a direction of 38 degree north of east. Determine the magnitude and direction of the components of the force that point along the north-south line and along east-west line. A speed skater goes around a turn with a 31 m radius. The skater has a speed of 14 m/s and experiences a centripetal force of 460 N. What is the mass of the skater? A 2 kg block is lifted vertically 2 m by a man What is work done by Kevin has a mass of 87- kg and is skating with in-line skates. He younger brother up ahead standing on the sidewalk, with his back tuned. Coming up, grabs his just before he brother and rolls off at a speed of 2.4 m/s. Ignoring friction, find Kevin just before he grabbed his brother. A disk (radius = 2.00: mm) is attached to a high-speed drill at a dentist's turning at 7.85 times 10^4 rad/s. Determine the tangential speed of a point on the outer his disk. A celling fan has two different angular speed setting: omega_1 = 440 rev/min and omega_2 what is the ratio a_1/a_2 of the centripetal accelerations of a given point on a blade? A particle is located at each corner of an imaginary cube. Each edge of the cube is and each particle has amass of 0.12 kg. What is the moment of inertia of these particle respect to an axis that lies along one edge of the cube? What is the unit of k (spring constant) in SI system? A 3500-kg statue is placed on top of a cylindrical concrete (Y = 2.3 times 10^10 N/m^2) stand. The stand has a cross-sectional area of 7.3 times 10^-2 m^2 and a height of 1.8m. By how much the statue compress the stand? An airplane wing is designed so that the speed of the air across the top of the wing is 251 when the speed of the air below the wing is 225 m/s. The density of the air is 1.29 kg/m^3

Explanation / Answer

6)

Work Done =(mg)xr=2x9.8x2 = 39.2J

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7)

Since momentum is conserved, the momentum Kevin has before he picks up his brother will = combined momentum after he picks him up.which is perfectly inelastic collision, the equation is :

mv(i) + mv(i) = (m + m)v(f)

Since his brother is initially at rest, his momentum is zero, so the mv(i) term is zero. Solved for v(i) :

v(i) = [(m + m)v(f)] / m
= [(87kg + 22kg)2.4m/s] / 87kg
= 3.0m/s

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8) Omega =v/r

so v=r=7.85x104 rad/s x.002=157m/s

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9)

centripetal accelaration= (w2)xr
r is same here. Only w1 and w2 are different.
So ratio is w12/w22

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11)It's N/m (Newtons per meter) because it's force per unit length

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12)

by elastic properties, Y = mg L / A e , where 'e' is the compression.

hence,
e = m g L / A Y = 3500x9.8 x 1.8 / 7.3x10^-2 x 2.3x10^10
= 36.8 x10^-6 m = 36.8 micro metre.

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