An impala is migrating across a field that has been fenced with a 180 cm fence.

Question

An impala is migrating across a field that has been fenced with a 180 cm fence. To escape it needs to jump this fence. Assume that the impala jumps the fence with just enough vertical velocity, v_0 to clear it. If the height (in cm) of the impala is given by h(t) = v_0t - 490t^2, then find the velocity v(t) = h'(t) of the impala at any time (in sec), t Greaterthanorequalto 0, before hitting the ground. Find when the velocity is equal to zero in terms of do- This is the time at the maximum height. Since the impala is 180 cm in the air at this time, use the equation for the height, h(t) to compute the initial velocity, v_0, with which the impala must launch itself to clear the fence. With the initial velocity computed above, determine how long the impala is in the air, when jumping over the fence.

Explanation / Answer

h'(t) = V - 980t

Since the impala barely makes it over the fence,
0 = V - 980t
V = 980t

180 = (980t)t - 490t²
180 = 490t²
t = 0.607 s

V = 980(0.607)
V = 594 cm/s

h'(t) = 594 - 980t

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