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.