Answer:
5 seconds
Explanation:
The straight line distance between (0, 0) and the antelope's position (x, y) at time t can be found using distance formula:
d² = x² + y²
d² = (-39 + 40t)² + (228 + 30t)²
d² = 1521 - 3120t + 1600t² + 51984 + 13680t + 900t²
d² = 53505 + 10560t + 2500t²
The cheetah can run a total distance of:
105 * 7 = 735
The time t at this distance is:
735² = 53505 + 10560t + 2500t²
540225 = 53505 + 10560t + 2500t²
0 = -486720 + 10560t + 2500t²
0 = -24336 + 528t + 125t²
t = 12, -16.224
t can't be negative, so t = 12.
Therefore, the cheetah can wait 5 seconds before it has to start running.
