An 88g arrow shot with Force=110N. Distance traveled is 78cm. What is speed of arrow?
To find the speed of the arrow, we can use the equation that relates force, mass, and acceleration. The equation is:
Force = mass × acceleration
In this case, the force is given as 110N (Newtons), and the mass of the arrow is 88g (grams) which is equivalent to 0.088kg (kilograms). We can rearrange the equation to solve for acceleration:
acceleration = force ÷ mass
Now, we need to find the acceleration of the arrow. To do this, we need to convert the distance traveled from centimeters to meters. Since 1 meter is equal to 100 centimeters, we can convert 78cm to meters by dividing it by 100:
distance traveled = 78cm ÷ 100 = 0.78m
We know that acceleration is defined as the change in velocity over time, but since we're trying to find the initial velocity (speed) of the arrow, we can assume that the final velocity is zero (assuming the arrow comes to a stop). Now, we can use another equation to find acceleration:
velocity² = initial velocity² + 2 × acceleration × distance
Since the final velocity is zero and assuming the arrow starts from rest, the equation simplifies to:
velocity² = 2 × acceleration × distance
Substituting the values we know:
velocity² = 2 × acceleration × 0.78m
Now, we can rearrange the equation to solve for acceleration:
acceleration = velocity² ÷ (2 × distance)
Plugging in the values, we have:
acceleration = 110N ÷ 0.088kg = 1250 m/s²
Now, we can substitute the acceleration back into the previous equation and solve for velocity:
velocity² = 2 × 1250 m/s² × 0.78m
velocity² = 1950 m²/s²
Taking the square root of both sides to solve for velocity:
velocity = √(1950 m²/s²) = 44.15 m/s
Therefore, the speed of the arrow is 44.15 m/s.