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What is the velocity of a mass of 75 kg about to hit the ground after falling 80 meters?
Wiki User
∙ 15y ago
Kinetic energy is defined as Ek= ½ m v². First, a free fall implies an acceleration of -9.81 m/s². If the initial height is 80 m, the final height is 0 m, the initial speed is 0 m/s, and the acceleration is -9.81 m/s², then the "free fall" time is about 4.039 s. The final speed will therefore be -39.62 m/s. The kinetic energy will be ½(75)(-39.62)² = 58,860 J. Second, 8 g is 0.008 kg. The kinetic energy of the bullet is ½(0.008)(1000)² = 4,000 J. The free falling person will have the greatest kinetic energy.
Wiki User
∙ 14y ago
Wiki User
∙ 15y agoThe equation you need to use here connects velocity, distance, and acceleration.
This is: V2 = U2 + 2 A x S. Here V = final velocity, U = initial velocity, A = acceleration, S = distance. In this case U = zero, asuming the mass is held stationary and then dropped. A = 9.81 meters/sec2, this is the earth's gravitational attraction. S = 80 meters
So V2 = 2 x 9.81 x 80 = 1569.6, V = 39.62 meters/sec (The mass is not relevant and does not enter the calculation. Did you hear the story of how Galileo dropped a large and a small cannonball simultaneously from the top of the leaning tower of Pisa, and showed that they reached the ground together?)
Wiki User
∙ 14y agoYou can calculate the final velocity of a hammer by using the following kinematics equation:
V2 = V02 + 2(a)(xf - xi)
(V is the final velocity, V0 is the initial velocity, a is the acceleration and xf is the final position and xi is the initial position. Notice how mass does not apply to free fall problems)
The object starts from rest, so V0=0. The acceleration is the acceleration due to gravity, 9.8 m/s2. The final position is at ground level, so xf = 0, and the object starts from xi = 42m.
V2 = 0 + 2(-9.8)(-42)
V2 = 823.2 m/s
V = sqrt(823.2 m/s)
V = -28.69 m/s
*Note that the final answer is negative. The equation used requires you to take a square root, and since a square root can never be negative, the answer came out positive. But, since the velocity is in the negative (down) direction, I had to add the negative sign afterwards.
Wiki User
∙ 12y ago7.5 meters per second
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