Butch and Sundance are standing on the edge of a cliff, arguing about whether or not they should jump into the water below. Butch drops a small rock and is able to count to 7-Mississippi (i.e., 7 seconds) before it hits the water. Assume g=10 m/s2. Ignore air resistance. a) If they were to jump, how fast would they be going just before they hit the water? (in m/s) b) How high is the cliff in meters? c) Transform the velocity in a) to mi/hr and the height in b) to feet. Would you jump?
Displacement, Velocity and Acceleration
In classical mechanics, kinematics deals with the motion of a particle. It deals only with the position, velocity, acceleration, and displacement of a particle. It has no concern about the source of motion.
Linear Displacement
The term "displacement" refers to when something shifts away from its original "location," and "linear" refers to a straight line. As a result, “Linear Displacement” can be described as the movement of an object in a straight line along a single axis, for example, from side to side or up and down. Non-contact sensors such as LVDTs and other linear location sensors can calculate linear displacement. Non-contact sensors such as LVDTs and other linear location sensors can calculate linear displacement. Linear displacement is usually measured in millimeters or inches and may be positive or negative.
Butch and Sundance are standing on the edge of a cliff, arguing about whether or
not they should jump into the water below. Butch drops a small rock and is able to count to 7-Mississippi (i.e., 7 seconds) before it hits the water. Assume g=10 m/s2.
Ignore air resistance.
a) If they were to jump, how fast would they be going just before they hit the water?
(in m/s)
b) How high is the cliff in meters?
c) Transform the velocity in a) to mi/hr and the height in b) to feet. Would you jump?
Given:-
Time required to reach the ball at the surface of water = 7s
g = 10m/s^2
As ball is dropped from the hand, initial velocity will be zero.
Take the downward direction from cliff towards the pond to be (+ve).
V(final velocity) = velocity at which rock hits the water = U( initial velocity ) + g(t)
V = 0+ 10×7 = 70m/s
Hence, velocity at which rock hits the water is = 70m/s.
The velocity is independent of the mass, They will hit the water surface with same velocity as rock hits.
Hence they will hit the water surface at 70m/s .
Now, for height ..use the relation.
V^2 = U^2 + 2×g × h ( U = initial velocity)
V= final velocity, h = height
(70)^2 = 0+ 2×10×h
Or h= height of cliff =( 70×70)/20 = 245 m.
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