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What is the maximum distance we can shoot a dart, provided our toy dart gun gives a maximum initial velocity of 7.33 m/s ? More information needed.

5.48 m
3.67 m
10.96 m


User Mondieki
by
8.5k points

1 Answer

5 votes

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.

User Jgravois
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8.0k points