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

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 $32.14 \, \text{m/s}$.

Steps to Solve

Identify the known values We have the initial velocity $V = 50 , \text{m/s}$ and the launch angle $\theta = 40^\circ$.
Use the sine function to find the vertical velocity The formula to find the vertical component of the velocity is given by: $$ V_v = V \cdot \sin(\theta) $$
Substitute the known values Now, substitute $V$ and $\theta$ into the equation: $$ V_v = 50 \cdot \sin(40^\circ) $$
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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