What is the formula to calculate the average horizontal speed of the grasshopper as it progresses down the road?

The average horizontal speed of the grasshopper as it progresses down the road is approximately 3.39 m/s. To find this speed, we can use the range formula for projectile motion which is:
R = (v² * sin(2θ)) / g
Where:
R is the range of the projectile
v is the initial velocity of the projectile
θ is the launch angle
g is the acceleration due to gravity (approximately 9.8 m/s²)
By rearranging the formula to solve for the initial velocity (v), we get:
v = √((R * g) / sin(2θ)
Substitute the given values:
R = 1.1 m
θ = 35°
g ≈ 9.8 m/s²
Calculate the average horizontal speed:
v = √((1.1 * 9.8) / sin(2 * 35°))
v ≈ 3.39 m/s
Therefore, the average horizontal speed of the grasshopper as it progresses down the road is approximately 3.39 m/s.

## Explanation:

The average horizontal speed of the grasshopper is determined by calculating the initial velocity at which the grasshopper launches itself at an angle of 35 degrees to achieve a range of 1.1 meters. By utilizing the range formula for projectile motion and substituting the given values, the average horizontal speed is approximately 3.39 m/s. This speed signifies how fast the grasshopper is moving horizontally as it progresses down the road.
**Formula Used:**
## R = (v² * sin(2θ)) / g

Where:
R = Range of the projectile
v = Initial velocity of the projectile
θ = Launch angle
g = Acceleration due to gravity
By rearranging the formula to solve for the initial velocity (v), the calculation is done using the given range (R), launch angle (θ), and acceleration due to gravity (g). Once the values are substituted, the calculation yields the average horizontal speed of the grasshopper.
In summary, the average horizontal speed of the grasshopper as it progresses down the road is approximately 3.39 m/s, showcasing the velocity at which the grasshopper moves horizontally during its motion.