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A fox fleeing from a hunter encounters a 0.695m tall fence and attempts to jump it. The fox jumps with initial velocity of7.25m/s at an angle of 45 degrees,

beginning the jump 2.19m from the fence. By how much does the fox clear the fence? Treat the fox as a particle. 
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1 Answer

This is a projectile problem with
vi   = 7.25 m/s
θ   = 45°
Δx = 2.19 m
vix = vicosθ
Δx = (vicosθ)t 
So the time instant when the fox reaches the fence is
t = Δx/vicosθ
viy = visinθ
Δy = (visinθ)t - ½gt2
So the height of the fox when it reaches the fence is
Δy = (visinθ)(Δx/vicosθ) - ½g(Δx/vicosθ)2
     = Δx tanθ - ½g(Δx/vicosθ)2
     = (2.19) tan45° - ½(9.81)[2.19/(7.25•cos45°)]2
     = 1.295 m
Therefore, the fox clears the fence by
Δy - hfence = 1.295 - 0.695 = 0.600 m