A fox fleeing from a hunter encounters a 0.630 m tall fence and attempts to jump it. The fox jumps with an initial velocity of 7.20 m/s at an angle of 45.0°, beginning the jump 2.18 m from the fence. How far does the fox clear the fence
See related Question: Tue,2-1-11,12:01pm
To find out how far the fox clears the fence, we'll need to analyze the vertical and horizontal components of its jump separately.
First, let's find the time it takes for the fox to reach the maximum height (when its vertical velocity becomes zero) using the vertical component of the jump:
In this case, we can use the equation: vf = vi + at, where vf is the final velocity, vi is the initial velocity, a is the acceleration, and t is the time.
Given:
vi = 7.20 m/s (initial velocity)
a = -9.8 m/s² (acceleration due to gravity; negative because it is acting in the opposite direction)
vf = 0 m/s (final velocity at maximum height)
Rearranging the equation, we have:
vf = vi + at
0 = 7.20 - 9.8t
Solving for t, we get:
9.8t = 7.20
t = 7.20 / 9.8
t ≈ 0.735 sec
Now, using the time it took to reach maximum height, let's find the maximum height (h) using the formula for vertical displacement:
h = viy * t + (1/2) * a * t^2, where viy is the vertical component of the initial velocity, a is the acceleration, and t is the time.
Given:
viy = vi * sinθ (vertical component of the initial velocity)
a = -9.8 m/s² (acceleration due to gravity)
Plugging in the values, we have:
h = (7.20 m/s * sin(45°)) * 0.735 sec + (1/2) * (-9.8 m/s²) * (0.735 sec)^2
Calculating this, we find:
h ≈ 1.964 m
Since the fence is 0.630 m tall, the fox clears it by h - fence height:
Clearance = 1.964 m - 0.630 m
Clearance ≈ 1.334 m
Therefore, the fox clears the fence by approximately 1.334 meters.