What is the initial vertical velocity of the t-shirt (in m/s)?

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Understand the Problem

The question is asking to calculate the initial vertical velocity of a t-shirt launched from a t-shirt launcher at a specific angle and initial velocity. This will require using the sine function from trigonometry, specifically the formula Vv = V * sin(θ), where V is the initial velocity and θ is the launch angle.

Answer

The initial vertical velocity of the t-shirt is approximately $32.14 \, \text{m/s}$.
Answer for screen readers

The initial vertical velocity of the t-shirt is approximately $32.14 , \text{m/s}$.

Steps to Solve

  1. Identify the known values We have the initial velocity $V = 50 , \text{m/s}$ and the launch angle $\theta = 40^\circ$.

  2. Use the sine function to find the vertical velocity The formula to find the vertical component of the velocity is given by: $$ V_v = V \cdot \sin(\theta) $$

  3. Substitute the known values Now, substitute $V$ and $\theta$ into the equation: $$ V_v = 50 \cdot \sin(40^\circ) $$

  4. Calculate the vertical component Using a calculator, find $\sin(40^\circ)$: $$ \sin(40^\circ) \approx 0.6428 $$

Then calculate: $$ V_v = 50 \cdot 0.6428 \approx 32.14 , \text{m/s} $$

The initial vertical velocity of the t-shirt is approximately $32.14 , \text{m/s}$.

More Information

This calculation provides the vertical component of the t-shirt's initial velocity, which influences how high it will go before descending.

Tips

  • Forgetting to use the sine function to find the vertical component.
  • Confusing the angle in degrees with radians. Make sure to use the correct mode (degrees) on the calculator.
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