A projectile with a mass of 43.0 kg is fired with an initial speed of 122 m/s at

Question

A projectile with a mass of 43.0 kg is fired with an initial speed of 122 m/s at an angle of 30.0° above the horizontal from a 118-m-high cliff and into a lake (take lake level to be y = 0 m).

(a) Determine the initial total mechanical energy of the system of the projectile and the earth.
J

(b) If, when the projectile is at its maximum height of y = 273 m, it is traveling 86.5 m/s, determine the change in internal energy due to air resistance as the projectile travels to the top of the trajectory.
J

(c) What is the speed of the projectile immediately before it hits the water if the change in internal energy due to air resistance is one and a half times as much when the projectile is going down as it was when going up?
m/s

Explanation / Answer

a) intial energy = kinetic energy+potential energy

Ei = 1/2mv^2+mgh = 1/2*43*122^2+43*9.8*118

Ei = 320006+49725.2

Ei = 369731.2 J

b) w tot = k2-k1

w other = k2-k1-wgravity

w other = 1/2m(86.5^2-122^2)-43*9.8(118-273)

w other = -159137.6+65317

w other = -93820.6 J

c) w other = k2-k1-w gravity

k2 = -1.5*93820.6+1/2*43*122^2+43*9.8*118

k2 = -140730.9+320006+49725.2 = 229000.3

v f = sqrt(2*229000.3/43) = 103.2 m/s

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