A shotput is launched at an angle of 40° above the horizontal with an initial velocity of 13.3 m/s. What is the initial vertical velocity of the shotput?
Understand the Problem
The question is asking us to calculate the initial vertical velocity of a shotput launched at a given angle and initial velocity. To find this, we will use the formula for the vertical component of velocity, which is calculated by multiplying the initial velocity by the sine of the launch angle. Thus, we will calculate: initial vertical velocity = initial velocity × sin(angle).
Answer
The initial vertical velocity is given by $v_{iy} = v_i \times \sin(\theta)$.
Answer for screen readers
The initial vertical velocity is calculated as:
$$ v_{iy} = v_i \times \sin(\theta) $$
Steps to Solve
- Identify the given values
We need the initial velocity and the launch angle. Let's denote:
- ( v_i ) as the initial velocity
- ( \theta ) as the launch angle
- Convert the angle to radians if necessary
If the angle ( \theta ) is given in degrees, we need to convert it to radians because most math functions in calculators and programming languages use radians. The formula for conversion is:
$$ \theta_{radians} = \theta_{degrees} \times \frac{\pi}{180} $$
- Calculate the vertical component of the velocity
The formula to find the initial vertical velocity ( v_{iy} ) is:
$$ v_{iy} = v_i \times \sin(\theta) $$
- Insert the values and calculate
Substitute the values for ( v_i ) and ( \theta ) into the equation calculated in the previous step.
- Final result
Perform the calculation to find the initial vertical velocity.
The initial vertical velocity is calculated as:
$$ v_{iy} = v_i \times \sin(\theta) $$
More Information
To find the initial vertical velocity, we rely on the sine function because it effectively gives us the vertical contribution of the initial velocity based on the launch angle. This approach is quite common in projectile motion analysis.
Tips
- Forgetting to convert degrees to radians when using a calculator.
- Misusing the sine function (e.g., switching it with cosine).
- Failing to use the correct initial velocity value.
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