Need Some Help with physic questions, thanks beforehand. 1) A 1.0-kg projectile

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Need Some Help with physic questions, thanks beforehand.

1)  A 1.0-kg projectile is fired from a point on the earth's surface at an angle ? = 450 with the horizontal and with an initial velocity v0 = 30 m/s.  Neglect any effects due to air resistance and find:

a. What is the kinetic energy of the projectile when it reaches the highest point on its trajectory?

b. How much work was done in firing the projectile?

2)  A roller coaster starts from rest at the top of an 18-m hill.  The car travels to the bottom of the hill and continues up the next hill that is 10.0 m high. How fast is the car moving at the top of the 10.0-m hill, if friction is ignored?

3) A block of mass m is released from rest at a height R above a horizontal surface.  The acceleration due to gravity is g.  The block slides along the inside of a frictionless circular hoop of radius R. Find and expression that gives the speed of the mass at the bottom of the hoop.

Explanation / Answer

a)
KE = 1/2 mUx^2 = (1/2)*1*30^2*cos(45)^2 = 225 joule. ANS. Ux = U cos(45) is the horizontal speed, which is constant over the trajectory. At max height Vy = 0, there is no vertical speed.

b) Work is converted into KE at launch = 1/2 mU^2 = (1/2)*1*30^2 = 450 Joules. ANS. U = v0.

2)V^2 =2g(H - h) = 2*9.8*8 so that V = sqrt(2*9.8*8) = 12.52198067 = 12.5 mps. ANS. H = 18 m, h = 10 m, and g is g.

3)Eg = -Ek

The lost in potential energy is equal to the gain in kinetic energy so you can set them equal to each other.

mgR = -1/2mv^2

solve for v

v= sqrt(2gR)

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