A cheetah is crouched in ambush 20m to the east of an observers blind. At time t=0 the cheetah charges an aeroplane in a cleaning 50m east of the observer. The cheetah runs along the straight line.

Incomplete.

20 m/s

To analyze the situation, we need to consider the distance and position of the cheetah, the observer's blind, and the airplane.

Given information:
- The cheetah is crouched in ambush 20m east of the observer's blind.
- The observer's blind is the reference point (let's call it point O).
- At time t=0, the cheetah charges towards the airplane, which is 50m east of the observer's blind.

To determine the cheetah's position at any time t, we need to consider its speed. Let's assume the cheetah's speed is constant.

If we consider the ground between the observer's blind and the airplane as a straight line, we can use the formula for distance to calculate the cheetah's position.

The distance traveled by the cheetah is given by the equation:
Distance = Speed x Time

Since the cheetah starts charging at t=0, the time is equal to t.

Let's set up a coordinate system. Assume the observer's blind (O) is at point (0,0) in this coordinate plane.

Now, at t=0, the cheetah is at point (20,0) (20m east of the observer's blind). The airplane is at point (70,0) (50m east of the observer's blind).

The equation for the cheetah's position at any time t would be:
Cheetah's position (x,0) = (20 + (Speed x t), 0)

To find the time it takes for the cheetah to reach the airplane, we need to consider their positions. At t=0, the cheetah is at (20,0), and the airplane is at (70,0). Since both are moving in the positive x-direction, the cheetah will eventually catch up to the airplane.

To find the time it takes for the cheetah to reach the airplane, we need to find the point when their x-coordinates are the same. Setting the cheetah's position equal to the airplane's position and solving for t, we have:

20 + (Speed x t) = 70

Simplifying the equation:
Speed x t = 70 - 20
Speed x t = 50

Now, if we know the speed of the cheetah, we can solve for t.

Please provide the speed of the cheetah, and I can calculate the time it takes for the cheetah to catch up to the airplane.