Question

A fox fleeing from a hunter encounters a 0.675 m tall fence and attempts to jump it. The fox jumps with an initial velocity of 7.50 m/s at an angle of 45.0°, beginning the jump 1.94 m from the fence. By how much does the fox clear the fence? Treat the fox as a particle.

Answer 1

Let us consider the upwards direction as positive and the downwards direction as negative.

Gravitational acceleration = g = -9.81 m/s²

Initial velocity of the fox = V = 7.5 m/s

Angle at which the fox jumps = = 45^o

Initial horizontal velocity of the fox = V_x = VCos = (7.5)Cos(45) = 5.303 m/s

Initial vertical velocity of the fox = V_y = VSin = (7.5)Sin(45) = 5.303 m/s

Time taken by the fox to reach the fence = T

Horizontal distance of the fox from the fence = R = 1.94 m

There is no horizontal force acting on the fox therefore the horizontal velocity of the fox remains constant.

R = V_xT

1.94 = (5.303)T

T = 0.366 sec

Height of the fox when it reaches the fence = H

H = 1.284 m

Height of the fence = h = 0.675 m

Height by which the fox clears the fence = h₀

h₀ = H - h

h₀ = 1.284 - 0.675

h₀ = 0.609 m

Height by which the fox clears the fence = 0.609 m