Basic Physics - Kinematics (Horizontal and Vertical Motion)

Question

Please do provide me a good step-by-step solution and a final answer... still having troubles with coping up with these.

You are at the top of a 500-meter-high building and you saw a zombie 750 meters away from the building. It is running towards your building at a constant speed of 3.0 m/s. If you are to kill it by dropping a big stone vertically to the ground, how far must the zombie away from the building before you drop the stone to kill it?

Thank you so much and God bless!

Answer 1

The stone will fall at g=9.8 m/s/s.

The time to fall to the ground is given by the standard equation for distance and acceleration:

s = s₀ + v₀t + ½at²

^{In this case, s}₀ ^{and v}₀ ^{are equal to 0 (there is no initial velocity or distance from your perspective, so the equation simplifies to}

s = ½at²

You know s (500m) and a (9.8 m/sec/sec). Solve for t.

The distance the zombie will run in that time is given by the equation for constant velocity:

s=vt

You know v (3 m/s) and t (from the calculation above). Solve for s.