Answer:
The maximum distance the dart can travel is approximately 5.48 meters.
Step-by-step explanation:
To determine the maximum distance a dart can be shot from a toy dart gun with a maximum initial velocity of 7.33 m/s, we need some additional information. Specifically, we need to know the launch angle at which the dart is fired.
The maximum range of a projectile (in this case, the dart) occurs when it is launched at an angle of 45 degrees with respect to the horizontal. This angle provides the maximum horizontal distance for a given initial velocity.
Assuming the dart is launched at an angle of 45 degrees, we can use the following formula to calculate the maximum distance (range) it can travel:
Range = (Initial Velocity^2 * sin(2 * Launch Angle)) / Gravity
Where:
Initial Velocity is 7.33 m/s (given)
Launch Angle is 45 degrees (maximum range angle)
Gravity is the acceleration due to gravity, approximately 9.81 m/s².
Let's plug in the values and calculate the maximum distance:
Range = (7.33^2 * sin(2 * 45)) / 9.81
Range ≈ (53.6889 * 1) / 9.81
Range ≈ 5.48 meters
So, with a maximum initial velocity of 7.33 m/s and assuming a launch angle of 45 degrees, the maximum distance the dart can travel is approximately 5.48 meters.