Average Horizontal Speed of a Grasshopper

What is the average horizontal speed of the grasshopper as it hops along the road?

Can you determine the average horizontal speed of a grasshopper based on its range and launch angle?

Answer:

The average horizontal speed of the grasshopper is 1.98 m/s.

Let's break down the calculation to determine the average horizontal speed of the grasshopper:

First, we decompose the grasshopper speed V into its horizontal and vertical velocities Vx and Vy:

Vx = V * cos(45°) = V * √2/2

Vy = V * sin(45°) = V * √2/2

Since Vx = Vy = v, we can proceed with the calculations.

Next, for the vertical movement, we utilize the formula for the change in speed during the entire movement:

Initial vertical speed (V0) = v

Final vertical speed = -v

Acceleration (a) = -9.8 m/s²

By solving the equations, we find that v = 4.9t

For the horizontal movement, the distance is equal to speed times time:

Distance = v * t = 4.9t * t = 4.9t²

Given that the distance is 0.8m, we can calculate the time (t = 0.404s).

Finally, we determine the average horizontal speed:

Average speed = distance/time = 0.8m / 0.404s = 1.98 m/s

Therefore, the average horizontal speed of the grasshopper is 1.98 m/s.