College

If a projectile is launched at a velocity of 40.8 m/s and a launch angle of 46.5 degrees, how high will the projectile go?

Please provide your answer in meters to one decimal place.

Answer :

Sure! To determine how high the projectile will go when launched, we need to calculate the maximum height it reaches. Here’s how we can do it step by step:

1. Understand the Given Values:
- Initial velocity ([tex]\(v\)[/tex]) = 40.8 m/s
- Launch angle = 46.5 degrees

2. Convert the Angle from Degrees to Radians:
- Since trigonometric calculations in physics are often done using radians, we need to convert the given angle from degrees to radians. The conversion formula is:
[tex]\[
\text{Radians} = \text{Degrees} \times \left( \frac{\pi}{180} \right)
\][/tex]

3. Calculate the Vertical Component of the Initial Velocity:
- The vertical component ([tex]\(v_y\)[/tex]) of the initial velocity is found using the sine of the angle:
[tex]\[
v_y = v \times \sin(\text{angle in radians})
\][/tex]

4. Use the Formula for Maximum Height:
- The formula to calculate the maximum height ([tex]\(H\)[/tex]) a projectile reaches is:
[tex]\[
H = \frac{v_y^2}{2g}
\][/tex]
- Here, [tex]\(g\)[/tex] is the acceleration due to gravity, which is approximately 9.81 m/s[tex]\(^2\)[/tex].

5. Calculate the Height:
- Plug the values into the formula to find the maximum height.

6. Round to One Decimal Place:
- After calculating, round your result to one decimal place to get the final answer.

Following these steps, the projectile reaches a maximum height of 44.6 meters.