A boy standing on a platform of height h above a water pool wants to jump into t
ID: 1837372 • Letter: A
Question
A boy standing on a platform of height h above a water pool wants to jump into the pool safely. The pool is a distance d from the edge of the platform. To clear the distance d, the boy starts from rest a distance x0 from the edge and runs towards a water pool with an acceleration that varies with time according to the equation: a(t) = ct^2 ,
where c is a constant. Suppose the boy jumps horizontally from the edge and just clears the distance d. Assume, the effects of air resistance are negligible. Express all answers in terms of x0 , c, h and fundamental constants.
a) Derive an expression for the velocity of the boy just before he jumps horizontally off the platform
b) Derive an expression for the horizontal distance d he needs to clear before landing safely in the water pool
Explanation / Answer
acceleration:
a = ct2
velocity is,
dv/dt = ct2
dv = ct2 dt
integrate the equation:
v = ct3/3 + c
at t = 0, v = 0, so c= 0
v = ct3/3
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the distance is,
dx/dt = ct3/3 + c
dx = [ct3/3 + c] dt
integrate the equation:
x = ct4/4 + ct +c'
at t= 0, x=0, so c' = 0
x = ct4/4 + ct
d = ct4/4 + ct
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