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,

Question

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

Answer 1

This is a projectile problem with

v_i   = 7.25 m/s

θ   = 45°

Δx = 2.19 m

 

x-direction

v_ix = v_icosθ

Δx = (v_icosθ)t 

 

So the time instant when the fox reaches the fence is

t = Δx/v_icosθ

 

y-direction

v_iy = v_isinθ

Δy = (visinθ)t - ½gt²

 

So the height of the fox when it reaches the fence is

Δy = (v_isinθ)(Δx/v_icosθ) - ½g(Δx/vicosθ)²

     = Δx tanθ - ½g(Δx/v_icosθ)²

     = (2.19) tan45° - ½(9.81)[2.19/(7.25•cos45°)]²

     = 1.295 m

 

Therefore, the fox clears the fence by

Δy - h_fence = 1.295 - 0.695 = 0.600 m